Preface

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Glossary

Complete List of Publications for the Adomian Decomposition Method

Monographs and textbooks

  1. Adomian, G. (1983), Stochastic Systems, Academic Press, New York, NY.
  2. R. Rach, Stochastic Systems (Book Review), Acta Applicandae Mathematica, May 1986, Vol. 6, No. 1, pp. 95--99.
  3. Adomian, G. (1986), Nonlinear Stochastic Operator Equations, Academic Press, Orlando, FL.
  4. Adomian, G. (1987), Stokhasticheskiye sistemy, Translated into Russian by N.G. Volkova, Mir Publishers, Moscow.
  5. Adomian, G. (1989), Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht.
  6. Adomian, G. (1994), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht.
  7. Bellman, R.E. and Adomian, G. (1985), Partial Differential Equations: New Methods for their Treatment and Solution, D. Reidel Publishing Co., Dordrecht, pp. 237--287.
  8. Bellomo, N. and Riganti, R. (1987), Nonlinear Stochastic System Analysis in Physics and Mechanics, World Scientific Publishing Co., Singapore and River Edge, NJ.
  9. Cherruault, Y. (1998), Modèles et méthodes mathématiques pour les sciences du vivant, Presses Universitaires de France, Paris, pp. 119-61, 256-264.
  10. Grzymkowski, R. (2010), Niek lasyczne metody rozwięzywania zagadnień przewodzenia ciepła, Wydawnictwo Politechniki Ślęskiej, Gliwice, pp. 142--187.
  11. Grzymkowski, R., Hetmaniok, E. and Słota, D. (2002), Wybrane metody obliczeniowe w rachunk u wariacyjnym oraz w równaniach róóniczk owych i całk owych, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego, Gliwice, pp. 173-246.
  12. Haldar, K., Decomposition Analysis Method in Linear and Nonlinear Differential Equations, Chapman and Hall/CRC, 2015.
  13. Keskin, A.Ü., Boundary Value Problems for Engineers with MATLAB Solutions, 2019, Springer International Publishing, New York.
  14. Koochi, A., Abadyan, M., Nonlinear Differential Equations in Micro/nano Mechanics: Application in Micro/Nano Structures and Electromechanical Systems, Elsevier, Amsterdam, 2020.
  15. Ray, Santanu Saha, Nonlinear Differential Equations in Physics: Novel Methods for Finding Solutions, Springer, New York, 2020.
  16. Serrano, S.E. (1997), Hydrology for Engineers, Geologists and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, HydroScience Inc., Lexington, KY.
  17. Serrano, S.E. (2001), Engineering Uncertainty and Risk Analysis: A Balanced Approach to Probability, Statistics, Stochastic Modeling, and Stochastic Differential Equations, HydroScience Inc., Lexington, KY.
  18. Serrano, S.E. (2010), Hydrology for Engineers, Geologists, and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, 2nd revised ed., HydroScience Inc., Ambler, PA.
  19. Serrano, S.E. (2011), Engineering Uncertainty and Risk Analysis: A Balanced Approach to Probability, Statistics, Stochastic Processes, and Stochastic Differential Equations, 2nd revised ed., HydroScience Inc., Ambler, PA.
  20. Serrano, S.E. (2016), Differential Equations: Applied Mathematical Modeling, Nonlinear Analysis, and Computer Simulation in Engineering and Science, HydroScience Inc., Ambler, Pennsylvania.
  21. Shingareva, I. and Lizárraga-Celaya, C. (2011), Solving Nonlinear Partial Differential Equations with Maple and Mathematica, Springer, New York, NY, pp. 227--242.
  22. Wazwaz, A.-M. (1997), A First Course in Integral Equations, World Scientific Publishing Co., Singapore and River Edge, NJ.
  23. Wazwaz, A.-M. (2002), Partial Differential Equations: Methods and Applications, A.A. Balkema, Lisse.
  24. Wazwaz, A.-M. (2009), Partial Differential Equations and Solitary Waves Theory, Higher Education Press, Beijing, and Springer, Berlin.
  25. Wazwaz, A.-M. (2011), Linear and Nonlinear Integral Equations: Methods and Applications, Higher Education Press, Beijing and Springer, Berlin.
  26. Zheng, L., Zhang, X., Modeling and Analysis of Modern Fluid Problems, 2017, Elsevier, New York.

 

A bibliography on Theses and Dissertations involving the ADM

  1. Adomian, G., Howard Hughes Fellow, (1961), Linear Stochastic Operators, Ph. D. Dissertation (Physics), University of California at Los Angeles, Los Angeles, CA, August 1961 and July 1963; Microfilm Accession No. AAT 6402269, ProQuest/UMI (University Microfilms Inc.), Ann Arbor, MI, February 1964.
  2. Abbaoui, K. (1995), “Thèse de l’Université Pierre et Marie Curie – Paris VI”, Les fondements mathématiques de la méthode décompositionnelle d’Adomian et application à la résolution de problèmes issus de la biologie et de la médicine, Université Pierre et Marie Curie – Paris VI, Paris, France, 4 October 1995.
  3. Abbaoui, K. (1997), “Thèse d’Etat – Université de Sétif”, La méthode décompositionnelle d’Adomian et ses applications, Université de Sétif, Sétif, Algeria, 15 December 1997.
  4. Abdelrazec, A. (2008), Adomian decomposition method: convergence analysis and numerical approximations, MSc thesis (Mathematics), McMaster University, Hamilton, Ontario, Canada, November 2008.
  5. Abushammala, Mariam B.H., Iterative methods for the numerical solutions of boundary value problems, Thesis of the American University of Sharjah College of Arts and Sciences, Sharjah United Arab Emirates, June 2014.
  6. Al-awawdah, E., The Adomian decomposition method for solving partial differential equations, M.SC. Thesis, Birzeit University, Palestine, 2016.
  7. Bate, A.M.,Mathematical models in eco-epidemiology, University of Bath, 2013.
  8. Chiu, C.-H. (2001), “Application of Adomian’s decomposition method on the analysis of nonlinear heat transfer and thermal stresses in the fins, PhD dissertation (Mechanical Engineering), National Cheng Kung University, Tainan City, Taiwan, November 2001, National Digital Library of theses and dissertations in Taiwan (NDLTD in Taiwan), available at: www.ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/ccd=GFzW1p/record?r1=1&h1=2
  9. Elrod, M. (1973), “Numerical methods for stochastic differential equations”, PhD dissertation (Mathematics), University of Georgia, Athens, GA, 1973, Microfilm Accession No. AAT 7404789, ProQuest/UMI (University Microfilms, Inc.), Ann Arbor, MI, March 1974.
  10. Gabet, L. (1992), “Thèse de l’École Centrale de Paris”, Modélisation de la diffusion des médicaments à travers les capillaries et dans les tissue à la suite dúne theorie injection et esquisse dúne theorie décompositionnelle et applications aux équations aux dérivées partielles, École Centrale Paris, Paris, France, 2 July, 1992.
  11. Hamzah Faisal Tomaizeh, Modified Adomian Decomposition Method For Differential Equations, Ph D Thesis, 2017.
  12. Holmquist, Sonia, An examination of the effectiveness of the Adomian Decomposition Method in fluid dynamic applications, University of Central Florida, Theses and Dissertations, Doctoral Dissertation (Open Access), 2007.
  13. Khelifa, S. (2002), “Thèse d’Etat – Université d’Alger”, Equations aux dérivées partielles et method décompositionnelle d’Adomian, Université d’Alger, Algiers, Algeria, 30 September 2002.
  14. Malakian, K. (1979), “Linear and nonlinear stochastic operators”, PhD dissertation (Mathematics), University of Georgia, Athens, GA, 1979, Microfilm Accession No. AAT 8001019, ProQuest/UMI (University Microfilms, Inc.), Ann Arbor, MI, January 1980.
  15. N’Dour, M. (1997), “Thèse de l’Université Pierre et Marie Curie – Paris VI”, Etude mathématique et numérique d’un modèle de compétition entre deux souches différentes et de la diffusion de germes dans l’eau: Application de la méthode décompositionnelle, Université Pierre et Marie Curie – Paris VI, France, 24 November 1997.
  16. Ngarhasta, N. (2003), “Thèse d’Etat – Université de Ouagadougou”, Etude numérique de qulques problèmes de diffusion et d’équations intégrals par la méthode décompositionnelle d’Adomian, Université de Ouagadougou, Ouagadougou, Burkina-Faso, 10 January 2003.
  17. Pujol, M.J. (2000), “Thèse d’Etat – Université d’Alicante”, Méthode d’Adomian appliqué à un problème biologique: Contrôle optimal, Universidad de Alicante, Alicante, Spain, 29 September 2000.
  18. Seng, V. (1997), “Thèse de l’Université Pierre et Marie – Paris VI”, Recherche de formes canoniques d’Adomian pour la résolution d’équations fonctionnelles non linéaires par la méthode décompositionnelle, Université Pierre et Marie Curie – Paris VI, Paris, France, 26 November 1997.
  19. Sibul, L.H. (1968), “Application of linear stochastic operator theory”, PhD dissertation (Electrical Engineering), Pennsylvania State University, University Park, PA, 1968, Microfilm Accession No. AAT 6914569, ProQuest/UMI (University Microfilms Inc.), Ann Arbor, MI, September 1969.
  20. Tomaizeh, H., Modified Adomian decomposition method for differential equations, M.Sc. Thesis, Hebron-Palestine, 2017.
  21. van Tonningen, S. (1994), “Simulation of CMOS circuit transients with the decomposition method”, PhD dissertation (Electrical Engineering), University of Colorado at Colorado Springs, Colorado Springs, CO, May 1994, Microfilm Accession No. AAT 9423084, ProQuest/UMI (University Microfilms Inc.), Ann Arbor, MI, October 1994.
  22. Ungani, T.P., The Adomian Decomposition Method Applied to Blood Flow through Arteries in the presence of a Magnetic Field, School of Computational and Applied Mathematics University of Witwatersrand. Johannesburg, South Africa, 2015.

Reference List for ADM, 1963

  1. Adomian, G., “Linear randomly-varying systems”, in Nomura, T. (Ed.), Proceedings of the Fourth International Symposium on Space Technology and Science, Tokyo, Japan, 1962, Japan Publications Trading Co., Tokyo, p. 634.
  2. Adomian, G., “Linear stochastic operators”, Reviews of Modern Physics, Vol. 35 No. 1, pp. 185-207.

Reference List for ADM, 1964

  1. Adomian, G. (1964), “Stochastic Green's functions”, in Bellman, R.E. (Ed.), Proceedings of Symposia in Applied Mathematics, Vol. XVI: Stochastic Processes in Mathematical Physics and Engineering; Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society, New York, New York, USA, April 30 - May 2, 1963, American Mathematical Society, Providence, RI, pp. 1-39.

Reference List for ADM, 1967

  1. Adomian, G. (1967), “Theory of random systems”, in Kožešnik, J. (Ed.), Transactions of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Prague, Czechoslovakia, August 31 - September 11, 1965, Academia, Prague and Academic Press, New York, pp. 205--222.

Reference List for ADM, 1970

  1. Adomian, G., “Random operator equations in mathematical physics. I”, Journal of Mathematical Physics, 1970, Vol. 11, No. 3, pp. 1069--1084. https://doi.org/10.1063/1.1665198

Reference List for ADM, 1971

  1. Adomian, G., “Linear random operator equations in mathematical physics. II”, Journal of Mathematical Physics, 1971, Vol. 12, No. 9, pp. 1944--1948. https://doi.org/10.1063/1.1665827
  2. Adomian, G., “Linear random operator equations in mathematical physics. III”, Journal of Mathematical Physics, 1971, Vol. 12, No. 9, pp. 1948-1955.
  3. Adomian, G., “Erratum: random operator equations in mathematical physics. I, (J. Math. Phys. Vol. 11, 1069 (1970))”, Journal of Mathematical Physics, 1971, Vol. 12, No. 7, p. 1446.
  4. Adomian, G., “Erratum: random operator equations in mathematical physics. I, (J. Math. Phys. Vol. 11, 1069 (1970))”, Journal of Mathematical Physics, 1971, Vol. 12, No. 9, p. 2031.
  5. Adomian, G., “The closure approximation in the hierarchy equations”, Journal of Statistical Physics, 1971, Vol. 3, No. 2, pp. 127--133.
  6. Adomian, G. and Sibul, L.H., “Propagation in stochastic media”, Proceedings of the 1971 Antennas and Propagation Society International Symposium, Vol. 9, IEEE, pp. 163-5, doi:10.1109/APS.1971.1150900

Reference List for ADM, 1972

  1. Adomian, G., “Addendum: linear random operator equations in mathematical physics. III, (J. Math. Phys. Vol. 12, 1948 (1971))”, Journal of Mathematical Physics, 1972, Vol. 13, No. 2, p. 272.
  2. Adomian, G. (1972), “Signal processing in a randomly time varying system”, Известия Академии Наук Армянской ССР; Серия: Математика, Vol. 7, No. 1, pp. 14-21.
  3. Adomian, G. (1972), “Addendum: Linear random operator equations in mathematical physics. III, [J. Math. Phys. 12, 1948 (1971)]”, Journal of Mathematical Physics, Vol. 13, No. 2, p. 272.

Reference List for ADM, 1975

  1. Adomian, G. (1975), “Obtaining first and second order statistics and in stochastic differential equations for the nonlinear case”, Известия Академии Наук Армянской ССР; Серия: Математика, Vol. 10, No. 6, pp. 529-534.

Reference List for ADM, 1976

  1. Adomian, G., Nonlinear stochastic differential equations, Journal of Mathematical Analysis and Applications, 1976, Vol. 55, Issue 2, pp. 441--452. https://doi.org/10.1016/0022-247X(76)90174-8

Reference List for ADM, 1977

  1. Adomian, G. (1977), “The solution of general linear and nonlinear stochastic systems”, in Rose, J. and Bilciu, C. (Eds.), Modern Trends in Cybernetics and Systems; in Three Volumes; Proceedings of the Third International Congress of Cybernetics and Systems, Bucharest, Romania, August 25 - 29, 1975; Volume II, Springer-Verlag, Berlin, pp. 203-214.
  2. Adomian, G. and Lynch, T., “Stochastic differential operator equations with random initial conditions”, Journal of Mathematical Analysis and Applications, 1977, Vol. 61, No. 1, pp. 216--226.
  3. Adomian, G. and Sibul, L.H., “Stochastic Green’s formula and application to stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1977, Vol. 60, No. 3, pp. 743--746.

Reference List for ADM, 1978

  1. Adomian, G., “On the existence of solutions for linear and nonlinear stochastic operator equations”, Journal of Mathematical Analysis and Applications, 1978, Vol. 62, No. 2, pp. 229-235.
  2. Adomian, G. (1978), “On the existence of solutions for linear and nonlinear stochastic operator equations”, Journal of Mathematical Analysis and Applications, Vol. 62, No. 2, pp. 229-235.
  3. Adomian, G. (1978), “New results in stochastic equations – The nonlinear case”, in Lakshmikantham, V. (Ed.), Nonlinear Equations in Abstract Spaces; Proceedings of an International Symposium on Nonlinear Equations in Abstract Spaces, University of Texas at Arlington, Arlington, TX, USA, June 8 - 10, 1977, Academic Press, New York, pp. 3-23.

Reference List for ADM, 1979

  1. Adomian, G. (1979), “A constructive method for linear and nonlinear stochastic partial differential equations”, in Lakshmikantham, V. (Ed.), Applied Nonlinear Analysis; Proceedings of an International Conference on Applied Nonlinear Analysis, University of Texas at Arlington, Arlington, TX, USA, April 20 - 22, 1978, Academic Press, New York, pp. 13-23.
  2. Adomian, G. (1979), “Stochastic operators and dynamical systems”, in Wang, P.C.C., Schoenstadt, A.L., Russak, B.I. and Comstock, C. (Eds.), Information Linkage between Applied Mathematics and Industry; Proceedings of the First Annual Workshop on the Information Linkage between Applied Mathematics and Industry, Naval Postgraduate School, Monterey, CA, USA, February 23 - 25, 1978, Academic Press, New York, pp. 581-596.
  3. Adomian, G. and Malakian, K., “Closure approximation error in the mean solution of stochastic differential equations by the hierarchy method”, Journal of Statistical Physics, 1979, Vol. 21, No. 2, pp. 181--189.
  4. Malakian, K. (1979), “Linear and nonlinear stochastic operators”, PhD dissertation (Mathematics), University of Georgia, Athens, GA, 1979, Microfilm Accession No. AAT 8001019, ProQuest/UMI (University Microfilms, Inc.), Ann Arbor, MI, January 1980.

Reference List for ADM, 1980

  1. Adomian, G. (1980), “On the modeling and analysis of nonlinear stochastic systems”, in: Avula, X.J.R., Bellman, R.E., Luke, Y.L. and Rigler, A.K. (Eds.), Proceedings of the Second International Conference on Mathematical Modelling, St. Louis, Missouri, July 11 - 13, 1979, Vols. I, II, University of Missouri-Rolla, Rolla, MO, pp. 29-44.
  2. Adomian, G. and Malakian, K., “Operator-theoretic solution of stochastic systems”, Journal of Mathematical Analysis and Applications, 1980, Vol. 76, No. 1, pp. 183--201.
  3. Adomian, G. and Malakian, K., “Inversion of stochastic partial differential operators – the linear case”, Journal of Mathematical Analysis and Applications, 1980, Vol. 77, No. 2, pp. 505--512.
  4. Adomian, G. and Malakian, K., “Self-correcting approximate solution by the iterative method for linear and nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1980, Vol. 76, No. 2, pp. 309--327.
  5. Adomian, G. and Malakian, K., “Stochastic analysis”, Mathematical Modelling, 1980, Vol. 1, No. 3, pp. 211--235.
  6. Bellman, R.E. and Adomian, G., “The stochastic Riccati equation”, Nonlinear Analysis: Theory, Methods and Applications, 1980, Vol. 4, No. 6, pp. 1131--1133.

Reference List for ADM, 1981

  1. Adomian, G., “On product nonlinearities in stochastic differential equations”, Applied Mathematics and Computation, Vol. 8 No. 1, pp. 79--82.
  2. Adomian, G., “Stochastic nonlinear modeling of fluctuations in a nuclear reactor – a new approach”, Annals of Nuclear Energy, Vol. 8 No. 7, pp. 329--330.
  3. Adomian, G. and Elrod, M., “Generation of a stochastic process with desired first- and second-order statistics”, Kybernetes, 1981, Vol. 10, No. 1, pp. 25--30.
  4. Adomian, G. and Malakian, K., “A comparison of the iterative method and Picard’s successive approximations for deterministic and stochastic differential equations, Applied Mathematics and Computation, 1981, Vol. 8, No. 3, pp. 187--204.
  5. Adomian, G. and Sarafyan, D., “Numerical solution of differential equations in the deterministic limit of stochastic theory”, Applied Mathematics and Computation, 1981, Vol. 8, No. 2, pp. 111--119.
  6. Adomian, G. and Sibul, L.H., “On the control of stochastic systems”, Journal of Mathematical Analysis and Applications, 1981, Vol. 83, No. 2, pp. 611--621.
  7. Adomian, G. and Sibul, L.H., “Symmetrized solutions for nonlinear stochastic differential equations”, International Journal of Mathematics and Mathematical Sciences, 1981, Vol. 4, No. 3, pp. 529--542, doi:10.1155/S0161171281000380

Reference List for ADM, 1982

  1. Adomian, G., “Stochastic model for colored noise”, Journal of Mathematical Analysis and Applications, 1982, Vol. 88, No. 2, pp. 607--609.
  2. Adomian, G., “On Green’s function in higher order stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1982, 1982, Vol. 88, No. 2, pp. 604--606.
  3. Adomian, G., “Solution of nonlinear stochastic physical problems”, Rendiconti del Seminario Matematico Università e Politecnico di Torino, 1982, Vol. 40, No. Special, pp. 7--22.
  4. Adomian, G., “Stabilization of a stochastic nonlinear economy”, Journal of Mathematical Analysis and Applications, 1982, Vol. 88, No. 1, pp. 306-17.
  5. Adomian, G. (1982), “Application of stochastic differential equations to economics”, in Stochastic Differential Equations; Proceedings of the "5-Tage-Kurs" of the USP Mathematisierung at Bielefeld University, Bielefeld, Germany, October 12 - 16, 1981; Materialien des Universitätsschwerpunktes Mathematisierung der Einzelwissenschaften, Vol. 38, Universität Bielefeld, Bielefeld, Germany.
  6. Adomian, G. and Bellman, R.E., “On the Itô equation”, Journal of Mathematical Analysis and Applications, 1982, Vol. 86, No. 2, pp. 476--478.
  7. Adomian, G. and Malakian, K., “Existence and uniqueness of statistical measures for solution processes for linear-stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1982, Vol. 89, No. 1, pp. 186--192.

Reference List for ADM, 1983

  1. Adomian, G., “Approximate calculation of Green’s functions”, Journal of Approximation Theory, 1983, Vol. 37, No. 2, pp. 119--124.
  2. Adomian, G., “Partial differential equations with integral boundary conditions”, Computers and Mathematics with Applications, 1983, Vol. 9, No. 3, pp. 443--445.
  3. Adomian, G., Bellomo, N. and Riganti, R., “Semilinear stochastic systems: analysis with the method of the stochastic Green’s function and application in mechanics”, Journal of Mathematical Analysis and Applications, 1983, Vol. 96, No. 2, pp. 330--340.
  4. Adomian, G. and Rach, R., Inversion of nonlinear stochastic operators, Journal of Mathematical Analysis and Applications, 1983, Vol. 91, No. 1, pp. 39--46.
  5. Adomian, G. and Rach, R., “Anharmonic oscillator systems”, Journal of Mathematical Analysis and Applications, 1983, Vol. 91, No. 1, pp. 229--236. https://doi.org/10.1016/0022-247X(83)90101-4
  6. Adomian, G. and Rach, R., “A nonlinear differential delay equation”, Journal of Mathematical Analysis and Applications, 1983, Vol. 91, No. 2, pp. 301--304.
  7. Adomian, G. and Rach, R., Nonlinear stochastic differential delay equations, Journal of Mathematical Analysis and Applications, 1983, Vol. 91, No. 1, pp. 94--101. https://doi.org/10.1016/0022-247X(83)90094-X
  8. Adomian, G., Sibul, L.H., and Rach, R., “Coupled nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1983, Vol. 92, No. 2, pp. 427--434.

Reference List for ADM, 1984

  1. Adomian, G., “A new approach to nonlinear partial differential equations”, Journal of Mathematical Analysis and Applications, 1984, Vol. 102, No. 2, pp. 420--434.
  2. Adomian, G., “Convergent series solution of nonlinear equations”, Journal of Computational and Applied Mathematics, 1984, Vol. 11, No. 2, pp. 225--230.
  3. Adomian, G., “On the convergence region for decomposition solutions”, Journal of Computational and Applied Mathematics, 1984, Vol. 11, No. 3, pp. 379--380.
  4. Adomian, G. and Adomian, G.E., “A global method for solution of complex systems”, Mathematical Modelling, 1984, Vol. 5, No. 4, pp. 251--263.
  5. Adomian, G. and Adomian, G.E., “A global method for solution of complex systems”, Mathematical Modelling, 1984, Vol. 5, No. 4, pp. 251--263.
  6. Adomian, G., Adomian, G.E. and Bellman, R.E., “Biological system interactions”, Proceedings of the National Academy of Sciences of the United States of America, 1984, Vol. 81, No. 9, pp. 2938--2940.
  7. Adomian, G. and Rach, R., “Light scattering in crystals”, Journal of Applied Physics, 1984, Vol. 56, No. 9, pp. 2592--2594.
  8. Adomian, G. and Rach, R., “On nonzero initial conditions in stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1984, Vol. 102, No. 2, pp. 363--264.
  9. Adomian, G. and Vasudevan, R., “A stochastic approach to inverse scattering in geophysical layers”, Mathematical Modelling, 1984, Vol. 5, No. 5, pp. 339--342.
  10. Rach, R., A convenient computational form for the Adomian polynomials, Journal of Mathematical Analysis and Applications, 1984, Volume 102, Issue 2, pages 415--419. https://doi.org/10.1016/0022-247X(84)90181-1

Reference List for ADM, 1985

  1. Adomian, G., “Discretization, decomposition and supercomputers”, Journal of Mathematical Analysis and Applications, 1985, Vol. 112, No. 2, pp. 487--496.
  2. Adomian, G., “New approaches to solution of national economy models and business cycles”, Kybernetes, 1985, Vol. 14, No. 4, pp. 221--223.
  3. Adomian, G., “Nonlinear stochastic dynamical systems in physical problems”, Journal of Mathematical Analysis and Applications, 1985, Vol. 111, No. 1, pp. 105--113.
  4. Adomian, G., “Random eigenvalue equations”, Journal of Mathematical Analysis and Applications, 1985, Vol. 111, No. 2, pp. 427--432.
  5. Adomian, G. and Adomian, G.E., “Cellular systems and aging models”, Computers and Mathematics with Applications, 1985, Vol. 11, Nos. 1/3, pp. 283--291.
  6. Adomian, G. and Rach, R., Application of the decomposition method to inversion of matrices, Journal of Mathematical Analysis and Applications, Volume 108, Issue 2, June 1985, Pages 409--421.
  7. Adomian, G. and Adomian, G.E., “Cellular systems and aging models”, Computers and Mathematics with Applications, 1985, Vol. 11, Nos. 1/3, pp. 283--291.
  8. Adomian, G., Bigi, D. and Riganti, R., “On the solutions of stochastic initial-value problems in continuum mechanics”, Journal of Mathematical Analysis and Applications, 1985, Vol. 110, No. 2, pp. 442--462.
  9. Adomian, G. and Rach, R., “Algebraic equations with exponential terms”, Journal of Mathematical Analysis and Applications, 1985, Vol. 112, No. 1, pp. 136--140.
  10. Adomian, G. and Rach, R., Application of the decomposition method to inversion of matrices, Journal of Mathematical Analysis and Applications, 1985, Vol. 108, No. 2, pp. 409--421.
  11. Adomian, G. and Rach, R., “An algorithm for transient dynamic analysis”, Transactions of the Society for Computer Simulation, 1985, Vol. 2, No. 4, pp. 321--327.
  12. Adomian, G. and Rach, R., Coupled differential equations and coupled boundary conditions, Journal of Mathematical Analysis and Applications, 1985, Vol. 112, No. 1, pp. 129--135. https://doi.org/10.1016/0022-247X(85)90279-3
  13. Adomian, G. and Rach, R., “Nonlinear differential equations with negative power nonlinearities”, Journal of Mathematical Analysis and Applications, 1985, Vol. 112, No. 2, pp. 497--501.
  14. Adomian, G. and Rach, R., Nonlinear plasma response, Journal of Mathematical Analysis and Applications, 1985, Vol. 111, No. 1, pp. 114--118. https://doi.org/10.1016/0022-247X(85)90204-5
  15. Adomian, G. and Rach, R., On the solution of algebraic equations by the decomposition method, Journal of Mathematical Analysis and Applications, 1985, Vol. 105, No. 1, pp. 141--166.
  16. Adomian, G. and Rach, R., Polynomial nonlinearities in differential equations, Journal of Mathematical Analysis and Applications, 1985, Vol. 109, No. 1, pp. 90--95. https://doi.org/10.1016/0022-247X(85)90178-7
  17. Adomian, G., Rach, R., and Sarafyan, D., On the solution of equations containing radicals by the decomposition method, Journal of Mathematical Analysis and Applications, 1985, Vol. 111, No. 2, pp. 423--426.
  18. Bellomo, N. and Monaco, R., A comparison between Adomian’s decomposition methods and perturbation techniques for nonlinear random differential equations, Journal of Mathematical Analysis and Applications, 1985, Vol. 110, No. 2, pp. 495--502. https://doi.org/10.1016/0022-247X(85)90311-7
  19. Bonzani, I. (1985), Analysis of stochastic van der Pol oscillations using the decomposition method, in: Wahlström, B., Henriksen, R. and Sundby, N.P. (Eds.), Proceedings of the 11th IMACS World Congress on System Simulation and Scientific Computation, Oslo, Norway, August 5 - 9, 1985, Vol. 4: Control systems and robotics; Large scale, complex and stochastic systems; Modelling, North-Holland Publishing Co., Amsterdam, pp. 257-260.
  20. Monaco, R., Riganti, R. (1985), Mathematical analysis of the stochastic dynamics of a spinning spherical satellite, Journal of Mathematical Analysis and Applications, 1985, Vol. 105, No. 1, pp. 258--271.
  21. Serrano, S.E., Unny, T.E. and Lennox, W.C. (1985a), Analysis of stochastic groundwater problems. Part I: deterministic partial differential equations in groundwater flow. A functional-analytic approach, Journal of Hydrology, 1985, Vol. 82, Nos 3/4, pp. 247-63. https://doi.org/10.1016/0022-1694(85)90020-4
  22. Serrano, S.E., Unny, T.E. and Lennox, W.C. (1985b), Analysis of stochastic groundwater flow problems. Part II: stochastic partial differential equations in groundwater flow. A functional-analytic approach, Journal of Hydrology, 1985, Vol. 82, Nos 3/4, pp. 265-84. https://doi.org/10.1016/0022-1694(85)90021-6
  23. Serrano, S.E., Unny, T.E. and Lennox, W.C. (1985c), Analysis of stochastic groundwater flow problems. Part III: approximate solution of stochastic partial differential equations, Journal of Hydrology, 1985, Vol. 82, Nos 3/4, pp. 285--306. https://doi.org/10.1016/0022-1694(85)90022-8

Reference List for ADM, 1986

  1. Adomian, G., “A new approach to the heat equation – an application of the decomposition method”, Journal of Mathematical Analysis and Applications, 1986, Vol. 113, No. 1, pp. 202--209.
  2. Adomian, G., “Application of the decomposition method to the Navier-Stokes equations”, Journal of Mathematical Analysis and Applications, 1986, Vol. 119, Nos 1/2, pp. 340--360.
  3. Adomian, G., “Inversion of matrices”, Mathematics and Computers in Simulation, 1986, Vol. 28, No. 2, pp. 151--153.
  4. Adomian, G., “Nonlinear equations with mixed derivatives”, Journal of Mathematical Analysis and Applications, 1986, Vol. 120, No. 2, pp. 734--736.
  5. Adomian, G., “Nonlinear hyperbolic initial value problem”, Journal of Mathematical Analysis and Applications, 1986, Vol. 120, No. 2, pp. 730--733.
  6. Adomian, G., “Solution of the Navier-Stokes equation – I”, Computers and Mathematics with Applications, 1986, Vol. 12, No. 11, Pt. A, pp. 1119--1124.
  7. Adomian, G., “Solution of Lanchester equation models for combat”, Journal of Mathematical Analysis and Applications, 1986, Vol. 114, No. 1, pp. 176--177.
  8. Adomian, G., “Solution of algebraic equations”, Mathematics and Computers in Simulation, 1986, Vol. 28, No. 2, pp. 155--157.
  9. Adomian, G., Stochastic water reservoir modeling, Journal of Mathematical Analysis and Applications, 1986, Vol. 115, No. 1, pp. 233--234.
  10. Adomian, G., Systems of nonlinear partial differential equations, Journal of Mathematical Analysis and Applications, 1986, Vol. 115, No. 1, pp. 235--238. https://doi.org/10.1016/0022-247X(86)90038-7
  11. Adomian, G., State-delayed matrix differential-difference equations, Journal of Mathematical Analysis and Applications, 1986, Vol. 114, No. 2, pp. 426--428.
  12. Adomian, G., The decomposition method for nonlinear dynamical systems, Journal of Mathematical Analysis and Applications, 1986, Vol. 120, No. 1, pp. 370--383. https://doi.org/10.1016/0022-247X(86)90223-4
  13. Adomian, G., Decomposition solution for Duffing and van der Pol oscillators, International Journal of Mathematics and Mathematical Sciences, 1986, Vol. 9, No. 4, pp. 731--732, http://dx.doi.org/10.1155/S016117128600087X
  14. Adomian, G. and Adomian, G.E., Solution of the Marchuk model of infectious disease and immune response, Mathematical Modelling, 1986, Vol. 7, Nos 5/8, pp. 803--807.
  15. Adomian, G. and Bellomo, N., On the Tricomi problem, Computers and Mathematics with Applications, 1986, Vol. 12, Nos 4/5, Pt. A, pp. 557--563. https://doi.org/10.1016/0898-1221(86)90181-1
  16. Adomian, G. and Malakian, K., “Existence of the inverse of a linear stochastic operator”, Journal of Mathematical Analysis and Applications, 1986, Vol. 114, No. 1, pp. 55--56.
  17. Adomian, G. and Rach, R., On the solution of nonlinear differential equations with convolution product nonlinearities, Journal of Mathematical Analysis and Applications, 1986, Vol. 114, No. 1, pp. 171--175. https://doi.org/10.1016/0022-247X(86)90074-0
  18. Adomian, G. and Rach, R., A coupled nonlinear system, Journal of Mathematical Analysis and Applications, 1986, Vol. 113, No. 2, pp. 510--513. https://doi.org/10.1016/0022-247X(86)90322-7
  19. Adomian, G. and Rach, R., A new computational approach for inversion of very large matrices, Mathematical Modelling, 1986, Vol. 7, Nos. 2/3, pp. 113--141. https://doi.org/10.1016/0270-0255(86)90041-2
  20. Adomian, G. and Rach, R., “Algebraic computation and the decomposition method”, Kybernetes, 1986, Vol. 15, No. 1, pp. 33--37.
  21. Adomian, G. and Rach, R., On composite nonlinearities and the decomposition method, Journal of Mathematical Analysis and Applications, 1986, Vol. 113, No. 2, pp. 504--509.
  22. Adomian, G. and Rach, R., On linear and nonlinear integro-differential equations, Journal of Mathematical Analysis and Applications, 1986, Vol. 113, No. 1, pp. 199--201. https://doi.org/10.1016/0022-247X(86)90343-4
  23. Adomian, G. and Rach, R., Solving nonlinear differential equations with decimal power nonlinearities, Journal of Mathematical Analysis and Applications, 1986, Vol. 114, No. 2, pp. 423--425. https://doi.org/10.1016/0022-247X(86)90094-6
  24. Adomian, G. and Rach, R., The noisy convergence phenomena in decomposition method solutions, Journal of Computational and Applied Mathematics, 1986, Vol. 15, No. 3, pp. 379--381. https://doi.org/10.1016/0377-0427(86)90228-1
  25. Bellomo, N. and Riganti, R., “Time evolution and fluctuations of the probability density and entropy function for a class of nonlinear stochastic systems in mathematical physics”, Computers and Mathematics with Applications, 1986, Vol. 12, No. 6, Pt. A, pp. 663--675.
  26. Bigi, D. and Riganti, R. (1986), “Solutions of nonlinear boundary value problems by the decomposition method”, Applied Mathematical Modelling, 1986, Vol. 10, No. 1, pp. 49--52.

Reference List for ADM, 1987

  1. Adomian, G., “Vibration in offshore structures: an analysis for the general nonlinear stochastic case – Part I”, Mathematics and Computers in Simulation, 1987, Vol. 29, No. 2, pp. 119--122.
  2. Adomian, G., “Vibration in offshore structures – Part II”, Mathematics and Computers in Simulation, 1987, Vol. 29, No. 5, pp. 351--356.
  3. Adomian, G., “Wave propagation in nonlinear media”, Applied Mathematics and Computation, 1987, Vol. 24, No.4, pp. 311--332.
  4. Adomian, G., “Semilinear wave equations”, Computers and Mathematics with Applications, 1987, Vol. 14, No. 6, pp. 497--499.
  5. Adomian, G., “Nonlinear oscillations in physical systems”, Mathematics and Computers in Simulation, 1987, Vol. 29, Nos. 3/4, pp. 275--284.
  6. Adomian, G., “A general approach to solution of partial differential equation systems”, Computers and Mathematics with Applications, 1987, Vol. 13, Nos. 9/11, pp. 741--747.
  7. Adomian, G., “A new approach to the Efinger model for a nonlinear quantum theory for gravitating particles”, Foundations of Physics, 1987, Vol. 17, No. 4, pp. 419--423.
  8. Adomian, G., “An investigation of the asymptotic decomposition method for nonlinear equations in physics”, Applied Mathematics and Computation, 1987, Vol. 24, No. 1, pp. 1--17.
  9. Adomian, G., “Modeling and solving physical problems”, Mathematical Modelling, 1987, Vol. 8, pp. 57--60.
  10. Adomian, G., “Modification of the decomposition approach to the heat equation”, Journal of Mathematical Analysis and Applications, 1987, Vol. 124, No. 1, pp. 290--291.
  11. Adomian, G., “Analytical solutions for ordinary and partial differential equations”, in Knowles, I.W. and Saito, Y. (Eds.), Differential Equations and Mathematical Physics; Proceedings of an International Conference, Birmingham, Alabama, USA, March 3-8, 1986, Lecture Notes in Mathematics (LNM), Vol. 1285, Springer, Berlin, pp. 1--15.
  12. Adomian, G. and Rach, R., “Explicit solutions for differential equations”, Applied Mathematics and Computation, 1987, Vol. 23, No. 1, pp. 49--59.
  13. Bellomo, N. and Sarafyan, D., On Adomian’s decomposition method and some comparisons with Picard’s iterative scheme, Journal of Mathematical Analysis and Applications, 1987, Vol. 123, No. 2, pp. 389--400.
  14. Bonzani, I., “On a class of nonlinear stochastic dynamical systems: analysis of the transient behaviour”, Journal of Mathematical Analysis and Applications, 1987, Vol. 126, No. 1, pp. 39--50.
  15. Bonzani, I. and Riganti, R., “Periodical solutions of nonlinear dynamical systems by decomposition method”, Mechanics Research Communications, 1987, Vol. 14, Nos 5/6, pp. 371--378.
  16. Rach, R. (1987a), “On continuous approximate solutions of nonlinear differential equations”, Journal of Mathematical Analysis and Applications, Vol. 128 No. 2, pp. 484-7.
  17. Rach, R., On the Adomian (decomposition) method and comparisons withPicard’s method, Journal of Mathematical Analysis and Applications, 1987, vol. 128, Issue 2, pp. 480–483. https://doi.org/10.1016/0022-247X(87)90199-5
  18. Riganti, R. (1987), “On a class of nonlinear dynamical systems: the structure of a differential operator in the application of the decomposition method”, Journal of Mathematical Analysis and Applications, Vol. 124 No. 1, pp. 189--199.
  19. Serrano, S.E. and Unny, T.E. (1987), “Predicting groundwater flow in a phreatic aquifer”, Journal of Hydrology, Vol. 95 Nos 3/4, pp. 241--268.

Reference List for ADM, 1988

  1. Adomian, G., “A general approach for complex systems”, Kybernetes, 1988, Vol. 17, No. 1, pp. 49--59.
  2. Adomian, G., “A new approach to Burger’s equation”, Physica D: Nonlinear Phenomena, 1988, Vol. 31, No. 1, pp. 65--69.
  3. Adomian, G., “A review of the decomposition method in applied mathematics”, Journal of Mathematical Analysis and Applications, 1988, Vol. 135, No. 2, pp. 501--444.
  4. Adomian, G., “An adaptation of the decomposition method for asymptotic solutions”, Mathematics and Computers in Simulation, 1988, Vol. 30, No. 4, pp. 325--529.
  5. Adomian, G., “Analysis of model equations of gas dynamics”, AIAA Journal, 1988, Vol. 26, No. 2, pp. 242--244.
  6. Adomian, G., “Analytic solutions for nonlinear equations”, Applied Mathematics and Computation, 1988, Vol. 26, No. 1, pp. 77--88.
  7. Adomian, G., “Application of decomposition to convection-diffusion equations”, Applied Mathematics Letters, 1988, Vol. 1, No. 1, pp. 7--9.
  8. Adomian, G., “Corrigenda and comment on ‘a general approach to solution of partial differential equation systems’”, Computers and Mathematics with Applications, 1988, Vol. 15, Nos. 6/8, p. 711.
  9. Adomian, G., “Elliptic equations and decomposition”, Computers and Mathematics with Applications, 1988, Vol. 15, No. 1, pp. 65--67.
  10. Adomian, G., “New approach to the analysis and control of large space structures”, AIAA Journal, 1988, Vol. 26, No. 3, pp. 377--380.
  11. Adomian, G., “Propagation in dissipative or dispersive media”, Journal of Computational and Applied Mathematics, 1988, Vol. 23, No. 3, pp. 395--396.
  12. Adomian, G., “Solving the nonlinear equations of physics”, Computers and Mathematics with Applications, 1988, Vol. 16, Nos 10/11, pp. 903--914.
  13. G. Adomian, M. Pandolfi, and R. Rach, An application of the decomposition method to the matrix Riccati equation in a neutron transport process, Journal of Mathematical Analysis and Applications, Volume 136, Issue 2, December 1988, Pages 557--567.
  14. Adomian, G. and Rach, R., “Evaluation of integrals by decomposition”, Journal of Computational and Applied Mathematics, 1988, Vol. 23, No. 1, pp. 99--101.
  15. Adomian, G., Rach, R., and Elrod, M., “The decomposition method applied to stiff systems”, Mathematics and Computers in Simulation, 1988, Vol. 30, No. 3, pp. 271--276.
  16. Sen, A.K., “An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction”, Journal of Mathematical Analysis and Applications, 1988, Vol. 131, No. 1, pp. 232--245.

Reference List for ADM, 1989

  1. Adomian, G., “Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations”, International Journal of Mathematics and Mathematical Sciences, 1989, Vol. 12, No. 1, pp. 137--144.
  2. Adomian, G., “Comments on a ‘counterexample’ to decomposition”, Journal of Computational and Applied Mathematics, 1989, Vol. 26, No. 3, pp. 375--376.
  3. Adomian, G., “Speculations on possible directions and applications for the decomposition method”, in Blaquiére, A. (Ed.), Modeling and Control of Systems in Engineering, Quantum Mechanics, Economics and Biosciences; Proceedings of the Third Bellman Continuum Work shop, Sophia Antipolis, France, June 13-14, 1988, Lecture Notes in Control and Information Sciences (LNCIS), 1989, Vol. 121, Springer, Berlin, pp. 479--495.
  4. Adomian, G., Elrod, M. and Rach, R., “A new approach to boundary value equations and application to a generalization of Airy’s equation”, Journal of Mathematical Analysis and Applications, 1989, Vol. 140, No. 2, pp. 554--568.
  5. Adomian, G. and Rach, R., “Analytic parametrization and the decomposition method”, Applied Mathematics Letters, 1989, Vol. 2, No. 4, pp. 311--313.
  6. Adomian, G., Rach, R., and Elrod, M., “On the solution of partial differential equations with specified boundary conditions”, Journal of Mathematical Analysis and Applications, 1989, Vol. 140, No. 2, pp. 569--581.
  7. Cherruault, Y. (1989), “Convergence of Adomian’s method”, Kybernetes, Vol. 18, No. 2, pp. 31--38.
  8. Datta, B.K. (1989), “A new approach to the wave equation – an application of the decomposition method”, Journal of Mathematical Analysis and Applications, 1989, Vol. 142, No. 1, pp. 6--12.
  9. Rach, R. (1989), “Decomposition solution of a proposed counterexample”, Applied Mathematics Letters, Vol. 2 No. 4, pp. 373-375.
  10. Rach, R. and Adomian, G. (1989), “Smooth polynomial expansions of piecewise-differentiable functions”, Applied Mathematics Letters, Vol. 2 No. 4, pp. 377-9.
  11. Rach, R. and Adomian, G. (1989), “Smooth polynomial expansions of piecewise-differentiable functions”, Applied Mathematics Letters, 1989, Vol. 2 No. 4, pp. 377--379.

Reference List for ADM, 1990

  1. Adomian, G., “Decomposition solution of nonlinear hyperbolic equations”, Mathematical and Computer Modelling, 1990, Vol. 14, pp. 80--82.
  2. Adomian, G. and Rach, R., “Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations”, Computers and Mathematics with Applications, 1990, Vol. 19, No. 12, pp. 9--12.
  3. Adomian, G. and Rach, R., “Purely nonlinear differential equations”, Computers and Mathematics with Applications, 1990, Vol. 20, No. 1, pp. 1--3.
  4. Baker, R. and Zeitoun, D.G., “Application of Adomian’s decomposition procedure to the analysis of a beam on random winkler support”, International Journal of Solids and Structures, 1990, Vol. 26, No. 2, pp. 217--235.
  5. Datta, B.K. (1990), “A technique for approximate solutions to Schrödinger-like equations”, Computers and Mathematics with Applications, 1990, Vol. 20, No. 1, pp. 61--65.
  6. Repaci, A., Nonlinear dynamical systems: the accuracy of Adomian's decomposition method, Appl. Math. Lett., 3 (1990), pp. 35-39
  7. Rach, R. and Adomian, G. (1990), “Multiple decompositions for computational convenience”, Applied Mathematics Letters, Vol. 3 No. 3, pp. 97--99.
  8. Rach, R. and Baghdasarian, A. (1990), “On approximate solution of a nonlinear differential equation”, Applied Mathematics Letters, Vol. 3 No. 3, pp. 101--102.
  9. Rèpaci, A. (1990), “Nonlinear dynamical systems: on the accuracy of Adomian’s decomposition method”, Applied Mathematics Letters, 1990, Vol. 3 No. 4, pp. 35--39.
  10. Serrano, S.E. (1990a), “Modeling infiltration in hysteretic soils”, Advances in Water Resources, Vol. 13 No. 1, pp. 12-23.
  11. Serrano, S.E. (1990b), “Using the C language to approximate non-linear stochastic systems”, Advances in Engineering Software, Vol. 12 No. 2, pp. 59-68.
  12. Serrano, S.E. and Unny, T.E. (1990), “Random evolution equations in hydrology”, Applied Mathematics and Computation, Vol. 38 No. 3, pp. 201-26.
  13. Yee, E. (1990), “An approximate analytical solution for the reaction-convection-diffusion equation”, Physics Letters A, Vol. 151 Nos 6/7, pp. 295-302.

Reference List for ADM, 1991

  1. Adomian, G., “A review of the decomposition method and some recent results for nonlinear equations”, Computers and Mathematics with Applications, 1991, Vol. 21, No. 5, pp. 101--127.
  2. Adomian, G., “An analytical solution of the stochastic Navier-Stokes system”, Foundations of Physics, 1991, Vol. 21, No. 7, pp. 831--843.
  3. Adomian, G., “Solving frontier problems modelled by nonlinear partial differential equations”, Computers and Mathematics with Applications, 1991, Vol. 22, No. 8, pp. 91--94.
  4. Adomian, G., “The sine-Gordon, Klein-Gordon and Korteweg-de Vries equations”, Computers and Mathematics with Applications, 1991, Vol. 21, No. 5, pp. 133--136.
  5. Adomian, G., “Errata to ‘a review of the decomposition method and some recent results for nonlinear equations’: (Computers Math. Applic., Vol. 21 No. 5, 1991, pp. 101-127)”, Computers and Mathematics with Applications, 1991, Vol. 22, No. 8, p. 95.
  6. Adomian, G. and Rach, R., “Linear and nonlinear Schrödinger equations”, Foundations of Physics, 1991, Vol. 21, No. 8, pp. 983--991.
  7. Adomian, G. and Rach, R., “Solution of nonlinear ordinary and partial differential equations of physics”, Journal of Mathematical and Physical Sciences, 1991, Vol. 25, Nos 5/6, pp. 703--718.
  8. Adomian, G. and Rach, R., Transformation of series, Applied Mathematics Letters, 1991, Vol. 4, No. 4, pp. 69-- 71. https://doi.org/10.1016/0893-9659(91)90058-4
  9. Adomian, G., Rach, R., and Meyers, R.E., “An efficient methodology for the physical sciences”, Kybernetes, 1991, Vol. 20, No. 7, pp. 24-34.
  10. Adomian, G., Rach, R., and Meyers, R.E., Numerical algorithms and decomposition, Computers and Mathematics with Applications, 1991, Vol. 22, No. 8, pp. 57--61. https://doi.org/10.1016/0898-1221(91)90013-T
  11. Baghdasarian, A., “Comments on the validity of a proposed counterexample on the method of decomposition”, Mechanics Research Communications, 1991, Vol. 18, No. 1, pp. 67--69. https://doi.org/10.1016/0093-6413(91)90030-Z

Reference List for ADM, 1992

  1. Adomian, G. and Rach, R., “A further consideration of partial solutions in the decomposition method”, Computers and Mathematics with Applications, 1992, Vol. 23, No. 1, pp. 51--64.
  2. Adomian, G. and Rach, R., “An approach to steady-state solutions”, Applied Mathematics Letters, 1992, Vol. 5, No. 5, pp. 39--40.
  3. Adomian, G. and Rach, R., “Generalization of Adomian polynomials to functions of several variables”, Computers and Mathematics with Applications, 1992, Vol. 24, Nos. 5/6, pp. 11--24.
  4. Adomian, G. and Rach, R., “Inhomogeneous nonlinear partial differential equations with variable coefficients”, Applied Mathematics Letters, 1992, Vol. 5, No. 2, pp. 11--12.
  5. Adomian, G. and Rach, R., “Modified decomposition solution of nonlinear partial differential equations”, Applied Mathematics Letters, Vol. 5 No. 6, pp. 29-30.
  6. Adomian, G. and Rach, R., “Noise terms in decomposition solution series”, Computers and Mathematics with Applications, 1992, Vol. 24, No. 11, pp. 61--64.
  7. Adomian, G. and Rach, R., “Nonlinear transformation of series – Part II”, Computers and Mathematics with Applications, 1992, Vol. 23, No. 10, pp. 79--83. https://doi.org/10.1016/0898-1221(92)90058-P
  8. Cherruault, Y., Saccomandi, G. and Some, B. (1992), “New results for convergence of Adomian’s method applied to integral equations”, Mathematical and Computer Modelling, 1992, Vol. 16, No. 2, pp. 85--93.
  9. Mavoungou, T. and Cherruault, Y. (1992), “Convergence of Adomian’s method and applications to nonlinear partial differential equations”, Kybernetes, Vol. 21 No. 6, pp. 13-25.
  10. Rach, R., Adomian, G. and Meyers, R.E. (1992), A modified decomposition, Computers and Mathematics with Applications, 1992, Vol. 23, No. 1, pp. 17--23. https://doi.org/10.1016/0898-1221(92)90076-T
  11. Rach, R., Baghdasarian, A. and Adomian, G. (1992), “Differential equations with singular coefficients”, Applied Mathematics and Computation, Vol. 47 Nos 2/3, pp. 179--184.

Reference List for ADM, 1993

  1. Adomian, G., “A class of nonlinear relativistic partial differential equations in elementary particle theory”, Foundations of Physics Letters, 1993, Vol. 6, No. 6, pp. 603--605.
  2. Adomian, G., “The N-body problem”, Foundations of Physics Letters, 1993, Vol. 6, No. 6, pp. 597--602.
  3. Adomian, G. and Meyers, R.E., “Nonlinear transport in moving fluids”, Applied Mathematics Letters, 1993, Vol. 6, No. 5, pp. 35--38.
  4. Adomian, G. and Rach, R., “A new algorithm for matching boundary conditions in decomposition solutions”, Applied Mathematics and Computation, 1993, Vol. 58, No. 1, pp. 61--68.
  5. Adomian, G. and Rach, R., “Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition”, Journal of Mathematical Analysis and Applications, 1993, Vol. 174, No. 1, pp. 118--137.
  6. Adomian, G. and Rach, R., “Solution of nonlinear partial differential equations in one, two, three and four dimensions”, World Scientific Series in Applicable Analysis, 1993, Vol. 2, pp. 1--13.
  7. Arora, H. and Abdelwahid, F., “Solution of non-integer order differential equations via the Adomian decomposition method”, Applied Mathematics Letters, 1993, Vol. 6, No. 1, pp. 21--23.
  8. Cherruault, Y. and Adomian, G. (1993), “Decomposition methods: a new proof of convergence”, Mathematical and Computer Modelling, 1993, Vol. 18, No. 12, pp. 103--106.
  9. Fang, J.-Q. (1993), “Inverse operator theory method and its applications in nonlinear physics”, Progress in Physics (Chinese Physical Society), 1993, Vol. 13 No. 4, pp. 441--560.
  10. Fang, J.-Q. and Yao, W.-G. (1993), “Inverse operator method for solutions of nonlinear dynamical equations and some typical applications”, Acta Physica Sinica, 1993, Vol. 42, No. 9, pp. 1375--1384.
  11. Gabet, L. (1993), “The decomposition method and linear partial differential equations”, Mathematical and Computer Modelling, 1993, Vol. 17, No. 6, pp. 11--22.
  12. Shawagfeh, N.T. (1993), “Nonperturbative approximate solution for Lane-Emden equation”, Journal of Mathematical Physics, 1993, Vol. 34 No. 9, pp. 4364--4369.
  13. Some, B. (1993), Some recent numerical methods for solving nonlinear Hammerstein integral equations, Mathematical and Computer Modelling, 1993, Vol. 18, No. 9, pp. 55--62. https://doi.org/10.1016/0895-7177(93)90142-L
  14. Yee, E. (1993), Application of the decomposition method to the solution of the reaction-convection-diffusion equation, Applied Mathematics and Computation, 1993, Vol. 56 No. 1, pp. 1-27. https://doi.org/10.1016/0096-3003(93)90075-P

Reference List for ADM, 1994

  1. Abbaoui, K. and Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Computers and Mathematics with Applications, 1994, Vol. 28, No. 5, pp. 103--109. https://doi.org/10.1016/0898-1221(94)00144-8
  2. Abbaoui, K. and Cherruault, Y., Convergence of Adomian’s method applied to nonlinear equations, Mathematical and Computer Modelling, 1994, Vol. 20, No. 9, pp. 60--73. https://doi.org/10.1016/0895-7177(94)00163-4
  3. Abbaoui, K. and Cherruault, Y., New ideas for solving identification and optimal control problems related to biomedical systems, International Journal of Bio-Medical Computing, 1994, Vol. 36, No. 3, pp. 181--186. https://doi.org/10.1016/0020-7101(94)90052-3
  4. Adomian, G., Solution of nonlinear evolution equations, Mathematical and Computer Modelling, 1994, Vol. 20, No. 12, pp. 1--2. https://doi.org/10.1016/0895-7177(94)90120-1
  5. Adomian, G., Solution of physical problems by decomposition, Computers and Mathematics with Applications, 1994, Vol. 27, Nos 9/10, pp. 145--154.
  6. Adomian, G., “The origin of chaos”, Foundations of Physics Letters, 1994, Vol. 7, No. 6, pp. 585--589.
  7. Adomian, G. and Efinger, H.J., “Analytic solutions for time-dependent Schrödinger equations with linear or nonlinear Hamiltonians”, Foundations of Physics Letters, 1994, Vol. 7, No. 5, pp. 489--491.
  8. Adomian, G. and Rach, R., “A new algorithm for solution of the harmonic oscillator by decomposition”, Applied Mathematics Letters, 1994, Vol. 7, No. 1, pp. 53--56.
  9. Adomian, G. and Rach, R., “Modified decomposition solution of linear and nonlinear boundary-value problems”, Nonlinear Analysis, Theory, Methods and Applications, 1994, Vol. 23, No. 5, pp. 615--619.
  10. Adomian, G., Rach, R., and Meyers, R.E., “Solution of generic nonlinear oscillators”, Applied Mathematics and Computation, 1994, Vol. 64, Nos 2/3, pp. 167--170.
  11. Cherruault, Y. (1994), “Convergence of decomposition methods and application to biological systems”, International Journal of Bio-Medical Computing, Vol. 36, No. 3, pp. 193--197.
  12. Gabet, L. (1994a), “The decomposition method and distributions”, Computers and Mathematics with Applications, 1994, Vol. 27, No. 3, pp. 41--49.
  13. Gabet, L. (1994b), The theoretical foundation of the Adomian method, Computers and Mathematics with Applications, Vol. 27, No. 12, pp. 41--52.
  14. Guellal, S. and Cherruault, Y. (1994), “Practical formulae for calculation of Adomian’s polynomials and application to the convergence of the decomposition method”, International Journal of Bio-Medical Computing, 1994, Vol. 36, No. 3, pp. 223--228.
  15. Mavoungou, T. and Cherruault, Y. (1994), “Numerical study of Fisher’s equation by Adomian’s method”, Mathematical and Computer Modelling, 1994, Vol. 19 No. 1, pp. 89-95.

Reference List for ADM, 1995

  1. Abbaoui, K. and Cherruault, Y., “New ideas for proving convergence of decomposition methods”, Computers and Mathematics with Applications, 1995, Vol. 29, No. 7, pp. 103--108.
  2. Abbaoui, K., Cherruault, Y., and N’Dour, M., “The decomposition method applied to differential systems”, Kybernetes, 1995, Vol. 24, No. 8, pp. 32--40.
  3. Abbaoui, K., Cherruault, Y. and Seng, V., Practical formulae for the calculus of multivariable Adomian polynomials, Mathematical and Computer Modelling, 1995, Vol. 22, No. 1, pp. 89--93.
  4. Adomian, G., “Solving the mathematical models of neurosciences and medicine”, Mathematics and Computers in Simulation, 1995, Vol. 40, Nos 1/2, pp. 107--114.
  5. Adomian, G., “A new approach to solution of the Maxwell equations”, Foundations of Physics Letters, 1995, Vol. 8, No. 6, pp. 583--587.
  6. Adomian, G., “Analytical solution of Navier-Stokes flow of a viscous compressible fluid”, Foundations of Physics Letters, 1995, Vol. 8, No. 4, pp. 389--400.
  7. Adomian, G., “Delayed nonlinear dynamical systems”, Mathematical and Computer Modelling, 1995, Vol. 22, No. 3, pp. 77--79.
  8. Adomian, G., “Fisher--Kolmogorov equation”, Applied Mathematics Letters, 1995, Vol. 8, No. 2, pp. 51--52.
  9. Adomian, G., “On integral, differential and integro-differential equations, perturbation and averaging methods”, Kybernetes, 1995, Vol. 24, No. 7, pp. 52--60.
  10. Adomian, G., “Random Volterra integral equations”, Mathematical and Computer Modelling, 1995, Vol. 22, No. 8, pp. 101--102.
  11. Adomian, G., “Stochastic Burgers’ equation”, Mathematical and Computer Modelling, 1995, Vol. 22, No. 8, pp. 103--105.
  12. Adomian, G., “The diffusion-Brusselator equation”, Computers and Mathematics with Applications, 1995, Vol. 29, No. 5, pp. 1--3.
  13. Adomian, G., “The Nikolaevskiy model for nonlinear seismic waves”, Mathematical and Computer Modelling, 1995, Vol. 22, No. 3, pp. 81--82.
  14. Adomian, G., “The generalized Kolmogorov--Petrovskii--Piskunov equation”, Foundations of Physics Letters, 1995, Vol. 8, No. 1, pp. 99--101.
  15. Adomian, G. and Meyers, R.E., “Generalized nonlinear Schrödinger equation with time-dependent dissipation”, Applied Mathematics Letters, 1995, Vol. 8, No. 6, pp. 7--8.
  16. Adomian, G. and Meyers, R.E., “Isentropic flow of an inviscid gas”, Applied Mathematics Letters, 1995, Vol. 8, No. 1, pp. 43--46.
  17. Adomian, G. and Meyers, R.E., “The Ginzburg-Landau equation”, Computers and Mathematics with Applications, 1995, Vol. 29, No. 3, pp. 3--4.
  18. Adomian, G. and Rach, R., “Kuramoto-Sivashinsky equation”, Journal of Applied Science and Computations, 1995, Vol. 1, No. 3, pp. 476--480.
  19. Adomian, G., Rach, R., and Shawagfeh, N.T., “On the analytic solution of the Lane-Emden equation”, Foundations of Physics Letters, 1995, Vol. 8, No. 2, pp. 161--181.
  20. Cherruault, Y., Adomian, G., Abbaoui, K. and Rach, R. (1995), “Further remarks on convergence of decomposition method”, International Journal of Bio-Medical Computing, Vol. 38, No. 1, pp. 89--93.
  21. George, A.J. and Chakrabarti, A. (1995), “The Adomian method applied to some extraordinary differential equations”, Applied Mathematics Letters, 1995, Vol. 8, No. 3, pp. 91--97.
  22. Guellal, S. and Cherruault, Y. (1995), “Application of the decomposition method to identify the distributed parameters of an elliptical equation”, Mathematical and Computer Modelling, 1995, Vol. 21, No. 4, pp. 51--55.
  23. Serrano, S.E. (1995), “Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity”, Water Resources Research, 1995, Vol. 31, No. 11, pp. 2733--2742.
  24. Sun, Y.-P., Xu, W.-L., Scott, K., An efficient method for solving the model equations of a two-dimensional packed bed electrode, J. Appl. Electrochem. 25 (1995) 755–763.
  25. van Tonningen, S. (1995), “Adomian’s decomposition method: a powerful technique for solving engineering equations by computer”, Computers in Education Journal, Vol. 5 No. 4, pp. 30--34.
  26. van Tonningen, S. and Ciletti, M.D. (1995), “ADM: a new technique for the simulation of CMOS circuit transients”, 1995 IEEE International Symposium on Circuits and Systems, Vol. 1, IEEE, pp. 732-5, doi:10.1109/ISCAS.1995.521621.
  27. Venkatarangan, S.N. and Rajalakshmi, K. (1995a), A modification of Adomian’s solution for nonlinear oscillatory systems, Computers and Mathematics with Applications, 1995, Vol. 29 No. 6, pp. 67-73. https://doi.org/10.1016/0898-1221(95)00008-M
  28. Venkatarangan, S.N. and Rajalakshmi, K. (1995b), Modification of Adomian’s decomposition method to solve equations containing radicals, Computers and Mathematics with Applications, 1995, Vol. 29 No. 6, pp. 75-80. https://doi.org/10.1016/0898-1221(95)00009-N
  29. Wazwaz, A.-M. (1995a), A new approach to the nonlinear advection problem: an application of the decomposition method, Applied Mathematics and Computation, 1995, Vol. 72 Nos 2/3, pp. 175--181.
  30. Wazwaz, A.-M. (1995b), The decomposition method for approximate solution of the Goursat problem, Applied Mathematics and Computation, 1995, Vol. 69 Nos 2/3, pp. 299-311. https://doi.org/10.1016/0096-3003(94)00137-S
  31. Wazwaz, A.-M. (1995c), “On the solution of the fourth order parabolic equation by the decomposition method”, International Journal of Computer Mathematics, Vol. 57 No. 3/4, pp. 213--217. https://doi.org/10.1080/00207169508804424

Reference List for ADM, 1996

  1. Adomian, G., “The Kadomtsev-Petviashvili equation”, Applied Mathematics and Computation, 1996, Vol. 76, No. 1, pp. 95--97.
  2. Adomian, G., “A non-perturbative solution of N-body dynamics”, Foundations of Physics Letters, 1996, Vol. 9, No. 3, pp. 301--308.
  3. Adomian, G., “Coupled Maxwell equations for electromagnetic scattering”, Applied Mathematics and Computation, 1996, Vol. 77, Nos 2/3, pp. 133--135.
  4. Adomian, G. (1996d), “Nonlinear Klein-Gordon equation”, Applied Mathematics Letters, 1996, Vol. 9, No. 3, pp. 9-10.
  5. Adomian, G., “Nonlinear random vibration”, Applied Mathematics and Computation, 1996, Vol. 77, Nos 2/3, pp. 109--112.
  6. Adomian, G., “Solution of coupled nonlinear partial differential equations by decomposition”, Computers and Mathematics with Applications, 1996, Vol. 31, No. 6, pp. 117--120.
  7. Adomian, G., “The Burridge--Knopoff model”, Applied Mathematics and Computation, 1996, Vol. 77, Nos 2/3, pp. 131--132.
  8. Adomian, G., “The dissipative sine-Gordon equation”, Foundations of Physics Letters, 1996, Vol. 9, No. 4, pp. 407--410.
  9. Adomian, G., “The fifth-order Korteweg-de Vries equation”, International Journal of Mathematics and Mathematical Sciences, 1996, Vol. 19, No. 2, p. 415, doi:10.1155/S0161171296000592
  10. Adomian, G., Cherruault, Y. and Abbaoui, K., “A nonperturbative analytical solution of immune response with time-delays and possible generalization”, Mathematical and Computer Modelling, 1996, Vol. 24, No. 10, pp. 89--96.
  11. Adomian, G. and Rach, R. (1996), “Modified Adomian polynomials”, Mathematical and Computer Modelling, 1996, Vol. 24, No. 11, pp. 39--46.
  12. Cho, Y.C. and Cho, N.Z. (1996), “Adomian decomposition method for point reactor kinetics problems”, Journal of the Korean Nuclear Society, Vol. 28, No. 5, pp. 452--457.
  13. Deeba, E.Y. and Khuri, S.A., “A decomposition method for solving the nonlinear Klein-Gordon equation”, Journal of Computational Physics, 1996, Vol. 124, pp. 442--448.
  14. Deeba, E.Y. and Khuri, S.A., The decomposition method applied to Chandrasekhar H-equation, Applied Mathematics and Computation, 1996, Vol. 77, No. 1, pp. 67--78. https://doi.org/10.1016/0096-3003(95)00188-3
  15. Haldar, K. and Datta, B.K. (1996), “Integrations by asymptotic decomposition”, Applied Mathematics Letters, 1996, Vol. 9, No. 2, pp. 81--83.
  16. Khuri, S.A. and Wazwaz, A.-M. (1996), “The decomposition method for solving a second kind Fredholm integral equation with a logarithmic kernel”, International Journal of Computer Mathematics, 1996, Vol. 61, Nos 1/2, pp. 103--110.
  17. Laffez, P. and Abbaoui, K. (1996), “Modelling of the thermic exchanges during a drilling. Resolution with Adomian’s decomposition method”, Mathematical and Computer Modelling, 1996, Vol. 23, No. 10, pp. 11--14.
  18. N’Dour, M., Abbaoui, K., Ammar, H., Cherruault, Y. (1996) “An example of an interaction model between two species”, Kybernetes, Vol. 25, No. 4, pp. 106--118.
  19. Rach, R. (1996), “Dr George Adomian – distinguished scientist and mathematician”, Kybernetes, Vol. 25 No. 9, pp. 45-50.
  20. Seng, V., Abbaoui, K. and Cherruault, Y. (1996), “Adomian’s polynomials for nonlinear operators”, Mathematical and Computer Modelling, 1996, Vol. 24 No. 1, pp. 59-65.
  21. Serrano, S.E. (1996), “Towards a nonperturbation transport theory in heterogeneous aquifers”, Mathematical Geology, Vol. 28 No. 6, pp. 701--721.
  22. Serrano, S.E. and Adomian, G. (1996), “New contributions to the solution of transport equations in porous media”, Mathematical and Computer Modelling, 1996, Vol. 24 No. 4, pp. 15-25.
  23. Shawagfeh, N.T. (1996), “Analytic approximate solution for a nonlinear oscillator equation”, Computers and Mathematics with Applications, Vol. 31 No. 6, pp. 135--141.
  24. Shawagfeh, N.T. and Adomian, G. (1996), “Non-perturbative analytical solution of the general Lotka-Volterra three-species system”, Applied Mathematics and Computation, Vol. 76 Nos 2/3, pp. 251-66.
  25. Venkatarangan, S.N. and Rajalakshmi, K., A modification of Adomian’s solution for nonlinear oscillatory systems, Computers & Mathematics with Applications, 1996, vol. 29, no. 6, pp. 67–73, 1995
  26. Wazwaz, A.-M. and Khuri, S.A. (1996), A reliable technique for solving the weakly singular second-kind Volterra- type integral equations, Applied Mathematics and Computation, 1996, Vol. 80 Nos 2/3, pp. 287--299. https://doi.org/10.1016/0096-3003(95)00279-0

Reference List for ADM, 1997

  1. Adomian, G., “Explicit solutions of nonlinear partial differential equations”, Applied Mathematics and Computation, 1997, Vol. 88, Nos. 2/3, pp. 117--126.
  2. Adomian, G., “Non-perturbative solution of the Klein--Gordon--Zakharov equation”, Applied Mathematics and Computation, 1997, Vol. 81, No. 1, pp. 89--92.
  3. Adomian, G., “On KdV type equations”, Applied Mathematics and Computation, 1997, Vol. 88, Nos. 2/3, pp. 131--135.
  4. Adomian, G., “On the dynamics of a reaction-diffusion system”, Applied Mathematics and Computation, 1997, Vol. 81, No. 1, pp. 93--95.
  5. Adomian, G., “Optical propagation in random media”, Applied Mathematics and Computation, 1997, Vol. 88, Nos. 2/3, pp. 127--129.
  6. Adomian, G., Rach, R., and Meyers, R.E., “Numerical integration, analytic continuation and decomposition”, Applied Mathematics and Computation, 1997, Vol. 88, Nos 2/3, pp. 95--116.
  7. Cherruault, Y. and Seng, V. (1997), “The resolution of non-linear integral equations of the first kind using the decompositional method of Adomian”, Kybernetes, Vol. 26, No. 2, pp. 198--206.
  8. Deeba, E.Y. and Khuri, S.A., The solution of nonlinear compartmental models, Mathematical and Computer Modelling, 1997, Vol. 25, No. 5, pp. 87--100. https://doi.org/10.1016/S0895-7177(97)00032-0
  9. Diţă, P. and Grama, N. (1997), On Adomian’s decomposition method for solving differential equations, Preprint. arXiv:solv-int/9705008
  10. Guellal, S., Grimalt, P., and Cherruault, Y., “Numerical study of Lorenz’s equation by the Adomian method”, Computers and Mathematics with Applications, 1997, Vol. 33, No. 3, pp. 25--29.
  11. N’Dour, M. (1997), “Thèse de l’Université Pierre et Marie Curie – Paris VI”, Etude mathématique et numérique d’un modèle de compétition entre deux souches différentes et de la diffusion de germes dans l’eau: Application de la méthode décompositionnelle, Université Pierre et Marie Curie – Paris VI, France, 24 November 1997.
  12. N’Dour, M. and Cherruault, Y. (1997), “The decomposition method applied to a diffusion model”, Kybernetes, 1997, Vol. 26, No. 8, pp. 921--935.
  13. Seng, V. (1997), “Thèse de l’Université Pierre et Marie – Paris VI”, Recherche de formes canoniques d’Adomian pour la résolution d’équations fonctionnelles non linéaires par la méthode décompositionnelle, Université Pierre et Marie Curie – Paris VI, Paris, France, 26 November 1997.
  14. Serrano, S.E. (1997a), “The Theis solution in heterogeneous aquifers”, Ground Water, Vol. 35 No. 3, pp. 463--467.
  15. Serrano, S.E. (1997b), Hydrology for Engineers, Geologists and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, HydroScience Inc., Lexington, KY.
  16. Wazwaz, A.-M. (1997a), Equality of partial solutions in the decomposition method for partial differential equations, International Journal of Computer Mathematics, 1997, Vol. 65 Nos 3/4, pp. 293-308; https://doi.org/10.1016/0898-1221(90)90246-G
  17. Wazwaz, A.-M. (1997b), Necessary conditions for the appearance of noise terms in decomposition solution series, Applied Mathematics and Computation, 1997, Vol. 81 Nos 2/3, pp. 265--274. https://doi.org/10.1016/S0096-3003(95)00327-4

Reference List for ADM, 1998

  1. Adomian, G., “Analytic solution of nonlinear integral equations of Hammerstein type”, Applied Mathematics Letters, 1998, Vol. 11, No. 3, pp. 127--130.
  2. Adomian, G., “Nonlinear dissipative wave equations”, Applied Mathematics Letters, 1998, Vol. 11, No. 3, pp. 125--126.
  3. Adomian, G., “Solution of the Thomas--Fermi equation”, Applied Mathematics Letters, Vol. 11, No. 3, pp. 131--133.
  4. Adomian, G., “Solutions of nonlinear P.D.E.”, Applied Mathematics Letters, 1998, Vol. 11, No. 3, pp. 121--123.
  5. Adomian, G. and Serrano, S.E., “Stochastic contaminant transport equation in porous media”, Applied Mathematics Letters, 1998, Vol. 11, No. 1, pp. 53--55.
  6. Andrianov, I.V., Olevskii, V.I., and Tokarzewski, S., “A modified Adomian’s decomposition method”, Journal of Applied Mathematics and Mechanics, 1998, Vol. 62, No. 2, pp. 309--314. https://doi.org/10.1016/S0021-8928(98)00040-9
  7. Deeba, E.Y. and Khuri, S.A. (1998a), “The solution of a two-compartment model”, Applied Mathematics Letters, 1998, Vol. 11, No. 1, pp. 1--6.
  8. Deeba, E.Y. and Khuri, S.A., “On the solution of some forms of the Korteweg-de Vries equation”, Applicable Analysis, 1998, Vol. 70, Nos 1/2, pp. 113--125.
  9. Hadizadeh, M. and Maleknejad, K. (1998), “On the decomposition method to the heat equation with non-linear and non-local boundary conditions”, Kybernetes, 1998, Vol. 27, No. 4, pp. 426--434.
  10. Khuri, S.A. (1998), “A new approach to the cubic Schrödinger equation: an application of the decomposition technique”, Applied Mathematics and Computation, 1998, Vol. 97, Nos 2/3, pp. 251--254.
  11. Mavoungou, T. and Cherruault, Y. (1998), “Solving frontier problems of physics by decomposition method: a new approach”, Kybernetes, Vol. 27 No. 9, pp. 1053--1061.
  12. Serrano, S.E. (1998), “Analytical decomposition of the nonlinear unsaturated flow equation”, Water Resources Research, Vol. 34 No. 3, pp. 397-407.
  13. Serrano, S.E. and Workman, S.R. (1998), “Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution”, Journal of Hydrology, Vol. 206 Nos 3/4, pp. 245--255.
  14. Vadasz, P. and Olek, S. (1998), “Transitions and chaos for free convection in a rotating porous layer”, International Journal of Heat and Mass Transfer, 1998, Vol. 41, No. 11, pp. 1417--1435.
  15. Wazwaz, A.-M., (1998a), A comparison between Adomian decomposition method and Taylor series method in the series solutions, Applied Mathematics and Computation, 1998, Vol. 97 No. 1, pp. 37-44. https://doi.org/10.1016/S0096-3003(97)10127-8
  16. Wazwaz, A.-M. (1998b), A reliable technique for solving the wave equation in an infinite one-dimensional medium, Applied Mathematics and Computation, 1998, Vol. 92 No. 1, pp. 1-7. https://doi.org/10.1016/S0096-3003(97)10037-6

Reference List for ADM, 1999

  1. Abbaoui, K. and Cherruault, Y., “The decomposition method applied to the Cauchy problem”, Kybernetes, 1999, Vol. 28, No. 1, pp. 68--74.
  2. Adjedj, B., “Application of the decomposition method to the understanding of HIV immune dynamics”, Kybernetes, 1999, Vol. 28, No. 3, pp. 271--283.
  3. Badredine, T., Abbaoui, K., and Cherruault, Y., “Convergence of Adomian’s method applied to integral equations”, Kybernetes, 1999, Vol. 28, No. 5, pp. 557--564.
  4. Golberg, M.A., A note on the decomposition method for operator equation, Applied Mathematics and Computation, 1999, 106, 215--220. https://doi.org/10.1016/S0096-3003(98)10124-8
  5. Hadizadeh, M. and Maleknejad, K., The numerical analysis of Adamian decomposition method for some nonlinear turbulent diffusion problems, Nonlinear Stud., 1999, Vol. 6, No. 1, pp. 85--89.
  6. Himoun, N., Abbaoui, K. and Cherruault, Y., “New results of convergence of Adomian’s method”, Kybernetes, 1999, Vol. 28, No. 4, pp. 423--429.
  7. Kaya, D., “On the solution of a Korteweg-de Vries like equation by the decomposition method”, International Journal of Computer Mathematics, 1999, Vol. 72 No. 4, pp. 531--539. https://doi.org/10.1080/00207169908804874
  8. Wazwaz, A.-M., A reliable modification of Adomian decomposition method, Applied Mathematics and Computation, 1999, vol. 102, no. 1, pp. 77–86, 1999.
  9. Wazwaz, A.-M. (1999a), A reliable modification of Adomian decomposition method, Applied Mathematics and Computation, 1999, Vol. 102 No. 1, pp. 77-86. https://doi.org/10.1016/S0096-3003(98)10024-3
  10. Wazwaz, A.-M. (1999b), Analytical approximations and Padé approximants for Volterra’s population model, Applied Mathematics and Computation, 1999, Vol. 100 No. 1, pp. 13-25.
  11. Wazwaz, A.-M. (1999c), The modified decomposition method and Padé approximants for solving the Thomas- Fermi equation, Applied Mathematics and Computation, 1999, Vol. 105 No. 1, pp. 11--19. https://doi.org/10.1016/S0096-3003(98)10090-5
  12. Wu, B.-T., Sun, Y.-P., A new exploration of the inverse operator solution for a kind of strong nonlinear partial differential equations with initial–boundary value conditions, Acta Mathematica Scientia 19(3) (1999) 347–355. (in Chinese)

Reference List for ADM, 2000

  1. Casasús, L. and Al-Hayani, W., “The method of Adomian for a nonlinear boundary value problem”, Revista de la Academia Canaria de Ciencias, 2000, Vol. 12, Nos 1/2, pp. 97--105.
  2. Deeba, E., Khuri, S.A. and Xie, S., An algorithm for solving a nonlinear integro-differential equation, Applied Mathematics and Computation, 2000, Vol. 115, Nos 2/3, pp. 123--131. https://doi.org/10.1016/S0096-3003(99)00124-1
  3. Deeba, E., Khuri, S.A. and Xie, S., An algorithm for solving boundary value problems, Journal of Computational Physics, 2000, Vol. 159, pp. 125--138. https://doi.org/10.1006/jcph.2000.6452
  4. Guellal, S., Cherruault, Y., Pujol, M.J., and Grimalt, P., “Decomposition method applied to hydrology”, Kybernetes, 2000, Vol. 29, No. 4, pp. 499--504.
  5. Kaya, D., An application of the decomposition method for second order wave equations, International Journal of Computer Mathematics, 2000, Vol. 75, No. 2, pp. 235--245.
  6. Khelifa, S. and Cherruault, Y., “New results for the Adomian method”, Kybernetes, 2000, Vol. 29, pp. 332--354.
  7. Ouedraogo, R.Z., Cherruault, Y. and Abbaoui, K. (2000), “Convergence of Adomian’s method applied to algebraic equations”, Kybernetes, 2000, Vol. 29 Nos 9/10, pp. 1298-305.
  8. Pujol, M.J. (2000), “Thèse d’Etat – Université d’Alicante”, Méthode d’Adomian appliqué à un problème biologique: Contrôle optimal, Universidad de Alicante, Alicante, Spain, 29 September 2000.
  9. Sanchez, F., Abbaoui, K. and Cherruault, Y. (2000), “Beyond the thin-sheet approximation: Adomian’s decomposition”, Optics Communications, Vol. 173 Nos 1/6, pp. 397-401.
  10. Serrano, S.E. and Workman, S.R. (2000a), “Reply to comment on ‘modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution’ by Serrano, S.E., Workman, S.R., (1998, Journal of Hydrology 206, 245-255)”, Journal of Hydrology, Vol. 235 Nos 3/4, pp. 293--296.
  11. Serrano, S.E. and Workman, S.R. (2000b), “Final remark on ‘modeling transient stream aquifer interaction with the non-linear Boussinesq equation and its analytical solution’ by Serrano, S.E., Workman, S.R., (1998, Journal of Hydrology 206, 245-255)”, Journal of Hydrology, Vol. 235 Nos 3/4, p. 298.
  12. Vadasz, P. and Olek, S. (2000), “Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equations”, International Journal of Heat and Mass Transfer, Vol. 43 No. 10, pp. 1715-34.
  13. Wazwaz, A.M. (2000a), A new algorithm for calculating Adomian polynomials for nonlinear operators, Applied Mathematics and Computation, 2000, vol. 111, Issue 1, pp. 33–51, 2000. doi>10.1016/S0096-3003(99)00063-6
  14. Wazwaz, A.-M. (2000b), A note on using Adomian decomposition method for solving boundary value problems, Foundations of Physics Letters, Vol. 13 No. 5, pp. 493-8.
  15. Wazwaz, A.-M. (2000c), Approximate solutions to boundary value problems of higher order by the modified decomposition method, Computers and Mathematics with Applications, Vol. 40 Nos 6/7, pp. 679--691. https://doi.org/10.1016/S0898-1221(00)00187-5
  16. Wazwaz, A.-M. (2000d), The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model, Applied Mathematics and Computation, 2000, Vol. 110 Nos 2/3, pp. 251-64. https://doi.org/10.1016/S0096-3003(99)00131-9
  17. Wazwaz, A.-M. (2000e), “The modified Adomian decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth-order”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 1, pp. 17-24. https://doi.org/10.1515/IJNSNS.2000.1.1.17
  18. Wazwaz, A.-M. (2000f), “The numerical solution of special eighth-order boundary value problems by the modified decomposition method”, Neural, Parallel and Scientific Computations, Vol. 8, pp. 133-46.
  19. Wazwaz, A.-M. (2000g), “The decomposition method for solving higher dimensional initial boundary value problems of variable coefficients”, International Journal of Computer Mathematics, Vol. 76 No. 2, pp. 159-72.
  20. Wazwaz, A.-M. (2000h), “The decomposition method for solving the diffusion equation subject to the specification of mass”, International Journal of Applied Mathematics, Vol. 3 No. 1, pp. 25-33.
  21. Wazwaz, A.-M. (2000i), Solitary wave solutions for the modified KdV equation by Adomian decomposition method, International Journal of Applied Mathematics, 2000, Vol. 3 No. 4, pp. 361-8.

Reference List for ADM, 2001

  2. Kaya, D., Explicit solution of a generalized nonlinear Boussinesq equation, J. Appl. Math. 1, 29-37, (2001).
  3. Khuri, S.A., A Laplace decomposition algorithm applied to class of non-linear differential equations, Journal of Applied Mathematics, 2001, Volume 1, Issue 4, Pages 141-155; http://dx.doi.org/10.1155/S1110757X01000183J.
  4. Madbouly, N.M., McGhee, D.F. and Roach, G.F. (2001), Adomian’s method for Hammerstein integral equations arising from chemical reactor theory, Applied Mathematics and Computation, 2001, Vol. 117 Nos 2/3, pp. 241-9.
  5. Serrano, S.E., Solute transport under non-linear sorption and decay, Water Research, International Associa- tion of Water Quality 35, 1525-1533, (2001).
  6. Serrano, S.E. (2001a), “Explicit solution to Green and Ampt infiltration equation”, Journal of Hydrologic Engineering, Vol. 6 No. 4, pp. 336--340.
  7. Serrano, S.E. (2001b), “Solute transport under non-linear sorption and decay”, Water Research, Vol. 35 No. 6, pp. 1525-33.
  8. Serrano, S.E. (2001c), Engineering Uncertainty and Risk Analysis: A Balanced Approach to Probability, Statistics, Stochastic Modeling, and Stochastic Differential Equations, HydroScience, Inc., Lexington, KY.
  9. Wazwaz, A.-M. (2001a), The numerical solution of fifth-order boundary value problems by the decomposition method, Journal of Computational and Applied Mathematics, 2001, Vol. 136, Nos 1/2, pp. 259--270. https://doi.org/10.1016/j.camwa.2009.03.073
  10. Wazwaz, A.-M. (2001b), The numerical solution of sixth-order boundary value problems by the modified decomposition method, Applied Mathematics and Computation, 2001, Vol. 118 Nos 2/3, pp. 311--325. https://doi.org/10.1016/S0096-3003(99)00224-6
  11. Wazwaz, A.-M. (2001c), “A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems”, Computers and Mathematics with Applications, Vol. 41 Nos 10/11, pp. 1237-44.
  12. Wazwaz, A.-M. (2001d), A reliable algorithm for solving boundary value problems for higher-order integro- differential equations, Applied Mathematics and Computation, 2001, Vol. 118 Nos 2/3, pp. 327--342. https://doi.org/10.1016/S0096-3003(99)00225-8
  13. Wazwaz, A.-M. (2001e), “A new algorithm for solving differential equations of Lane-Emden type”, Applied Mathematics and Computation, 2001, Vol. 118, Nos 2/3, pp. 287-310. https://doi.org/10.1016/S0096-3003(99)00223-4
  14. Wazwaz, A.-M. (2001f), “A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation”, Applied Mathematics and Computation, Vol. 123 No. 2, pp. 205-17.
  15. Wazwaz, A.-M. (2001g), “A reliable technique for solving linear and nonlinear Schrödinger equations by Adomian decomposition method”, Bulletin of the Institute of Mathematics (Academia Sinica), Vol. 29 No. 2, pp. 125-34.
  16. Wazwaz, A.-M. (2001h), “A study of nonlinear dispersive equations with solitary-wave solutions having compact support”, Mathematics and Computers in Simulation, Vol. 56 No. 3, pp. 269-76.
  17. Wazwaz, A.-M. (2001i), “Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions”, Applied Mathematics and Computation, Vol. 123 No. 1, pp. 133-40.
  18. Wazwaz, A.-M. (2001j), “Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method”, Chaos, Solitons and Fractals, 2001, Vol. 12 No. 12, pp. 2283-93.
  19. Wazwaz, A.-M. (2001k), “Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method”, Chaos, Solitons and Fractals, 2001, Vol. 12, No. 8, pp. 1549--1556.
  20. Wazwaz, A.-M. (2001l), “Exact solutions to nonlinear diffusion equations obtained by the decomposition method”, Applied Mathematics and Computation, 2001, Vol. 123, No. 1, pp. 109-22.
  21. Wazwaz, A.-M. (2001m), “The modified decomposition method applied to unsteady flow of gas through a porous medium”, Applied Mathematics and Computation, Vol. 118 Nos 2/3, pp. 123-32.
  22. Wazwaz, A.-M. (2001n), “Analytic treatment for variable coefficient fourth-order parabolic partial differential equations”, Applied Mathematics and Computation, Vol. 123 No. 2, pp. 219-27.
  23. Wazwaz, A.-M. (2001o), “A reliable algorithm for higher-dimensional diffusion equation subject to the specification of mass”, International Journal of Applied Mathematics, Vol. 7 No. 3, pp. 265-73.
  24. Wazwaz, A.M., El-Sayed, S.M., A new modification of the Adomian decomposition method for linear and nonlinear operators, Applied Mathematics and Computation, 2001, Volume 122, Issue 3, 15 August 2001, Pages 393-405; https://doi.org/10.1016/S0096-3003(00)00060-6

Reference List for ADM, 2002

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  4. Evans, D.J., Bulut, H., A new approach to the gas dynamics equation, an application of the decomposition method, Appl. Comput. Math., 79 (7) (2002), pp. 817--822.
  5. Jiao, T.C., Yamamoto, Y., Dang, C., Hao, Y., An Aftertreatment Technique for Improving the Accuracy of Adornian’s Decomposition Method, An lntemationai Journal Computers & Mathematics with Applications, 2002, Vol. 43 (2002) pp. 783-798
  6. Machado, J.M. and Tsuchida, M. (2002), Solutions for a class of integro-differential equations with time periodic coefficients, Applied Mathematics E-Notes, 2002, Vol. 2, pp. 66-71
  7. Mamaloukas, C., Haldar, K. and Mazumdar, H.P. (2002), Application of double decomposition to pulsatile flow, Journal of Applied Mathematics and Computing, 2002, Vol. 10 Nos 1/2, pp. 193-207.
  8. Ngarhasta, N., Some, B., Abbaoui, K., and Cherruault, Y., New numerical study of Adomian method applied to a diffusion model, Kybernetes, 2002, vol. 31, no. 1, pp. 61–75, 2002.
  9. Ngarasta, N., Some, B., Abbaoui, K. and Cherruault, Y. (2002), “New numerical study of Adomian method applied to a diffusion model”, Kybernetes, 2002, Vol. 31 No. 1, pp. 61-75.
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  11. Shawagfeh, N.T. (2002), Analytical approximate solutions for nonlinear fractional differential equations, Applied Mathematics and Computation, 2002, Vol. 131 Nos 2/3, pp. 517--529. https://doi.org/10.1016/S0096-3003(01)00167-9
  12. Wazwaz, A.-M. (2002a), A new method for solving singular initial value problems in the second-order ordinary differential equations, Applied Mathematics and Computation, 2002, Vol. 128, No. 1, pp. 45-57. https://doi.org/10.1016/S0096-3003(01)00021-2
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  14. Wazwaz, A.-M. (2002c), “The numerical solution of special fourth-order boundary value problems by the modified decomposition method”, International Journal of Computer Mathematics, Vol. 79 No. 3, pp. 345--356. https://doi.org/10.1080/00207160211928
  15. Wazwaz, A.-M. (2002d), Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional spaces, Applied Mathematics and Computation, 2002, Vol. 130, Nos 2/3, pp. 415--424. https://doi.org/10.1016/S0096-3003(01)00109-6

Reference List for ADM, 2003

  1. Abbasbandy, S., Improving Newton–Raphson methodfor nonlinear equations by modifiedAdomian decomposition method, Applied Mathematics and Computation, 2003, Vol. 145, Issues 2-3, pp. 887--893.
  2. Abdelwahid, F., A mathematical model of Adomian polynomials, Applied Mathematics and Computation, 2003, vol. 141, pp. 447--453.
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  4. Biazar, J., Babolian, E., Kember, G., Nouri, A., Islam, R., An alternate algorithm for computing Adomian polynomials in special cases, Applied Mathematics and Computation, 2003, Volume 138, Issues 2–3, 20 June 2003, Pages 523--529; https://doi.org/10.1016/S0096-3003(02)00174-1
  5. Biazar, J., Babolian, E., Islam, R., Solution of a system of Volterraintegral equations of the first kind by Adomian method, Applied Mathematics and Computation, 2003, Volume 139, Issues 2-3, pages 249--258; https://doi.org/10.1016/S0096-3003(02)00173-X
  6. Birregah, B., Some, B., Mampassi, B., New formulation of Adomian polynomials applied to Hamilton--Jacobi equations, Far East Journal of Applied Mathematics, 2003, Vol. 11,
  7. Choi, H.-W., and Shin, J.G., Symbolic implementation of the algorithm for calculating Adomian polynomials, Applied Mathematics and Computation, 2003, Volume 146, Issue 1, 30 December 2003, Pages 257--271; https://doi.org/10.1016/S0096-3003(02)00541-6
  8. Haldar, K., Application of Adomian's approximation to blood flow through arteries in the presence of a magnetic field, Journal of Applied Mathematics and Computing, 2003, vol. 12, No. 1-2, pp. 267--279.
  9. Himoun, N., Abbaoui, K., Cherruault, Y., “Short new results on Adomian methodd”, Kybernetes, 2003, Vol. 32, pp. 523--539.
  10. Liu, S.-B., Sun, Y.-P., S., Scott, K., Analytic Solution of Diffusion-Reaction in Spherical Porous Catalyst, Chemical Engineering & Technology, 2003, Vol. 26, No. 1, pp. 87--95; doi: 10.1002/ceat.200390013
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  12. Pujol, M.J. and Grimalt, P. (2003), “A non-linear model of cerebral diffusion stability of finite differences method and resolution using the Adomian method”, International Journal of Numerical Methods for Heat and Fluid Flow, 2003, Vol. 13 No. 4, pp. 473-485.
  13. Serrano, S.E. (2003a), “Improved decomposition solution to Green and Ampt equation”, Journal of Hydrologic Engineering, Vol. 8 No. 3, pp. 158-60.
  14. Serrano, S.E. (2003b), “Modeling groundwater flow under transient nonlinear free surface”, Journal of Hydrologic Engineering, Vol. 8 No. 3, pp. 123-32.
  15. Serrano, S.E. (2003c), “Propagation of nonlinear reactive contaminants in porous media”, Water Resources Research, Vol. 39 No. 8, pp. 1228-42.
  16. Shi-Bin, L., Yan-Ping, S., Scott, K., Analytic Solution of Diffusion-Reaction in Spherical Porous Catalyst, Chemical Engineering & Technology, 2003, Vol. 26, No. 1, pp. 87--95; doi: 10.1002/ceat.200390013
  17. Wazwaz, A.-M. (2003a), An analytic study on the third-order dispersive partial differential equations, Applied Mathematics and Computation, 2003, Vol. 142, Nos 2/3, pp. 511--520. https://doi.org/10.1016/S0096-3003(02)00336-3
  18. Wazwaz, A.-M. (2003b), The existence of noise terms for systems of inhomogeneous differential and integral equations, Applied Mathematics and Computation, 2003, Vol. 146, No. 1, pp. 81-92. https://doi.org/10.1016/S0096-3003(02)00527-1

Reference List for ADM, 2004

  1. Babolian, E., Biazar, J., and Vahidi, A., “Solution of a system of nonlinear equations by Adomian decomposition method,” Applied Mathematics and Computation, 2004, Vol. 153, Issue 3, pp. 847--854. doi: 10.1016/S0096-3003(03)00313-8
  2. Babolian, E. and Javadi, Sh., “New method for calculating Adomian polynomials”, Applied Mathematics and Computation, 2004, Volume 153, Issue 1, 25 May 2004, Pages 253--259. https://doi.org/10.1016/S0096-3003(03)00629-5
  3. Babolian, E., Javadi, S., and Sadehi, H., “Restarted Adomian Method for Integral Equations,” Applied Mathematics and Computation, 2004, Vol. 153, No. 2, 2004, pp. 353-359. doi:10.1016/S0096-3003(03)00636-2
  4. Belhaj, H., Biazar, J., Butt, S., Islam, R., Adomian Solution of Forchheimer Model to Describe Porous Media Flow, SPE/DOE Symposium on Improved Oil Recovery, 17-21 April, Tulsa, Oklahoma, 2004. https://doi.org/10.2118/89426-MS
  5. Biazar, J., Babolian, E., Islam, R., “Solution of the system of ordinary differential equations by Adomian decomposition method”, Applied Mathematics and Computation, 2004, Volume 147, Issue 3, 16 January 2004, Pages 713-719; https://doi.org/10.1016/S0096-3003(02)00806-8
  6. Bulut, H, Ergüt, M., Asil, V., and Bokor, R.H., Numerical solution of a viscous incompressible flow problem through an orifice by Adomian decomposition method, Appl. Math. Comput., 153 (2004), 733 - 741. https://doi.org/10.1016/s0096-3003(03)00667-2
  7. Chen, W., and Lu, Z., An algorithm for Adomian decomposition method, Applied Mathematics and Computation, 2004, Vol. 159, No. 1, (2004) pp. 221--235.
  8. M. Dehghan, Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications, Applied Mathematics and Computation, 2004, vol. 157, no. 2, pp. 549–560, 2004; https://doi.org/10.1016/j.amc.2003.08.098
  9. M. Dehghan, “The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure,” International Journal of Computer Mathematics, 2004, vol. 81, no. 8, pp. 979–989, 2004.
  10. M. Dehghan, “The use of Adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications,” International Journal of Computer Mathematics, 2004, vol. 81, no. 1, pp. 25–34, 2004.
  11. El-Sayed, S.M., Kaya, D., Zarea, S., The Decomposition Method applied to solve high-order linear Volterra-Fredholm integro differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 2004, Vol. 5, Issue 2, pp. 105--112. https://doi.org/10.1515/IJNSNS.2004.5.2.105
  12. El-Tawila, M.A., Bahnasawi, A.A., Abdel-Nabya, A., Solving Riccati differential equation using Adomian's decomposition method, Applied Mathematics and Computation, 2004, Volume 157, Issue 2, 5 October 2004, Pages 503-514; https://doi.org/10.1016/j.amc.2003.08.049
  13. Inc, M., On numerical solution of partial differential equations by the decomposition method, Kragujevac J. Math, 2004, Vol. 6, pp. 153--164.
  14. Ismail, H.N.A., Raslan, K., Rabboh, A.A.A., Adomian decomposition methodfor Burger’s–Huxley andBurger’s–Fisher equations, Applied Mathematics and Computation, 2004, Vol. 159, pp. 291–301
  15. Ismail, H.N.A., Raslan, K.R., Salem, G.S.E., Solitary wave solutions for the general KDV equation by Adomian decomposition method, Applied Mathematics and Computation, 2004, Vol. 159, pp. 291–301; doi: 10.1016/S0096-3003(03)00686-6
  16. Khuri, S.A., A new approach to Bratus problem, Applied Mathematics and Computation, 2004, 147 (1) (2004) 131–136.
  17. Raslan, K.R. (2004), “The decomposition method for a Hirota-Satsuma coupled KdV equation and a coupled MKdV equation”, International Journal of Computer Mathematics, 2004, Vol. 81 No. 12, pp. 1497-505.
  18. Ray, S.S. and Bera, R.K. (2004), “Solution of an extraordinary differential equation by Adomian decomposition method”, Journal of Applied Mathematics, Vol. 4, pp. 331--338.
  19. Serrano, S.E. (2004), “Modeling infiltration with approximate solutions to Richard’s equation”, Journal of Hydrologic Engineering, 2004, Vol. 9 No. 5, pp. 421--432.
  20. Shawagfeh, N.T. and Kaya, D. (2004a), Series solution to the Pochhammer-Chree equation and comparison with exact solutions, Computers and Mathematics with Applications, 2004, Vol. 47 No. 12, pp. 1915--1920.
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  22. Sonnad, J.R. and Goudar, C.T. (2004), “Solution of the Haldane equation for substrate inhibition enzyme kinetics using the decomposition method”, Mathematical and Computer Modelling, Vol. 40 Nos 5/6, pp. 573--582.
  23. Sun, Y.-P., Liu, S.-B. and Scott, K. (2004), “Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method”, Chemical Engineering Journal, 2004, Vol. 102 No. 1, pp. 1--10. https://doi.org/10.1016/S1385-8947(03)00060-3
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  26. Wazwaz, A.-M. (2004), The existence of noise terms for systems of inhomogeneous differential and integral equations, Applied Mathematics and Computation, 2004, Vol. 149 No. 1, pp. 15-29.
  27. Wazwaz, A.-M. and Gorguis, A. (2004a), An analytic study of Fisher’s equation by using Adomian decomposition method, Applied Mathematics and Computation, 2004, Vol. 154 No. 3, pp. 609--620. https://doi.org/10.1016/S0096-3003(03)00738-0
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Reference List for ADM, 2005

  1. Abbasbandy, S., “Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, 2005, Vol. 170, No. 1, pp. 648--656.
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  50. Wazwaz, A.-M. (2005a), Adomian decomposition method for a reliable treatment of the Bratu-type equations, Applied Mathematics and Computation, 2005, Vol. 166 No. 3, pp. 652--663. https://doi.org/10.1016/j.amc.2004.06.059
  51. Wazwaz, A.-M. (2005b), “Adomian decomposition method for a reliable treatment of the Emden-Fowler equation, Applied Mathematics and Computation, Vol. 161, No. 2, pp. 543-60.
  52. Wazwaz, A.-M. (2005c), Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method, Applied Mathematics and Computation, 2005, Vol. 166 No. 3, pp. 638-51. https://doi.org/10.1016/j.amc.2004.06.058
  53. Wazwaz, A.-M. (2005d), “The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations”, International Journal of Computer Mathematics, 2005, Vol. 82 No. 9, pp. 1107--1115.
  54. Yan, Z. (2005), Approximate Jacobi elliptic function solutions of the modified KdV equation via the decomposition method, Applied Mathematics and Computation, 2005, Vol. 166 No. 3, pp. 571-583. ttps://doi.org/10.1016/j.amc.2004.07.004
  55. Zhang, X. (2005), A modification of the Adomian decomposition method for a class of nonlinear singular boundary value problems, Journal of Computational and Applied Mathematics, 2005, Vol. 180 No. 2, pp. 377--389. https://doi.org/10.1016/j.cam.2004.11.007
  56. Zhu, Y., Chang, Q. and Wu, S. (2005), A new algorithm for calculating Adomian polynomials, Applied Mathematics and Computation, 2005, Vol. 169 No. 1, pp. 402--416. https://doi.org/10.1016/j.amc.2004.09.082

Reference List for ADM, 2006

  1. Abbasbandy, S., (2006) Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method, Applied Mathematics and Computation, 2006, Vol. 172, Issue 1, pp. 431--438; https://doi.org/10.1016/j.amc.2005.02.015
  2. Abbasbandy, S., Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method, Applied Mathematics and Computation, 2006, Vol. 172(1): pp. 485--490. https://doi.org/10.1016/j.amc.2005.02.014
  3. Abbasbandy, S., Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method, Applied Mathematics and Computation, 2006, Vol. 173, Issue 1, pp. 493--500. https://doi.org/10.1016/j.amc.2005.04.077
  4. Afrouzi, G.A. and Khademloo, S., On Adomian decomposition method for solving reaction diffusion equation, International Journal of Nonlinear Science, 2006, Vol. 2, No. 1, pp. 11--15.
  5. Al-Hayani, W. and Casasús, L., “On the applicability of the Adomian method to initial value problems with discontinuities”, Applied Mathematics Letters, 2006, Vol. 19, No. 1, pp. 22--31.
  6. Attili, B.S. and Lesnic, D., “An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems”, Applied Mathematics and Computation, 2006, Vol. 182, No. 2, pp. 1247--1254.
  7. Biazar, J. (2006), “Solution of the epidemic model by Adomian decomposition method”, Applied Mathematics and Computation, 2006, Vol. 173, No. 2, pp. 1101--1106.
  8. Biazar, J., Pourabd, M., A Maple program for computing Adomian polynomials, International Mathematical Forum, 2006, Vol. 1, no. 39, pp. 1919--1924.
  9. Bastro, M., Semiao, V., Calheiros, F., A new iterative method to compute nonlinear equations, Applied Mathematics and Computation, 2006, Vol. 173, Issue 1, pp. 468--483. https://doi.org/10.1016/j.amc.2005.04.045
  10. Biazar, J., Agha, R., and Islam, M.R. (2006), The Adomian decomposition method for the solution of the transient energy equation in rocks subjected to laser irradiation, Iranian Journal of Science and Technology, Transaction A: Science, 2006, Vol. 30, No. A2, pp. 201--212.
  11. Biazar, J. and Ayati, Z., An approximation to the solution of parabolic equation by Adomian decomposition method and comparing the result with Crank-Nicolson method, International Mathematical Forum, 2006, Vol. 1 No. 39, pp. 1925--1933.
  12. Biazar, J., Ilie, M. and Khoshkenar, A., “An improvement to an alternate algorithm for computing Adomian polynomials in special cases”, Applied Mathematics and Computation, 2006, Vol. 173, No. 1, pp. 582--592.
  13. Biazar, J. and Pourabd, M., A Maple program for computing Adomian polynomials, International Mathematical Forum, 2006, Vol. 1 No. 39, pp. 1919--1924 .
  14. Bildik, N., Konuralp, A., Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations, International Journal of Computer Mathematics, 2006, Volume 83, Issue 12, pp. 973--987. https://doi.org/10.1080/00207160601173407
  15. Bildik, N. and Konuralp, A., “The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations.” International Journal of Nonlinear Sciences and Numerical Simulation, 2006, Vol. 7, Issue 1, pp. 65--70; https://doi.org/10.1515/IJNSNS.2006.7.1.65
  16. Bougoffa, L., “Adomian method for a class of hyperbolic equations with an integral condition”, Applied Mathematics and Computation, 2006, Vol. 177, No. 2, pp. 545--552.
  17. Bougoffa, L., Solvability of the predator and prey system with variable coefficients and comparison of the results with modified decomposition, Applied Mathematics and Computation, 2006, Vol. 182, No. 1, pp. 383--387. https://doi.org/10.1016/j.amc.2006.02.050
  18. Bougoffa, L. and Bougouffa, S., Adomian method for solving some coupled systems of two equations, Applied Mathematics and Computation, 2006, Vol. 177, No. 2, pp. 553--160.
  19. Cafagna, D. and Grassi, G., “Hyperchaotic 3D-scroll attractors via Hermite polynomials: the Adomian decomposition approach”, in Proceedings of the 2006 IEEE International Symposium on Circuits and Systems (ISCAS 2006), 21-24 May 2006, IEEE, doi:10.1109/ISCAS.2006.1692684.
  20. Çelik, E., Bayram, M., Yeloğlu, T., Solution of Differential-Algebraic Equations(DAEs) by Adomian Decomposition Method, International Journal Pure & Applied Mathematical Sciences, 2006, ISSN 0972-9828 Vol.3, No.1, pp. 93-100
  21. Chun, C. (2006), A new iterative method for solving nonlinear equations, Applied Mathematics and Computation, Vol. 178, No. 2, pp. 415--422. https://doi.org/10.1016/j.amc.2005.11.055
  22. Daftardar-Gejji, V. and Jafari, H., An iterative method for solving nonlinear functional equations, Journal of Mathematical Analysis and Applications, 2006, Vol. 316, No. 2, pp. 753--763. https://doi.org/10.1016/j.jmaa.2005.05.009
  23. Dehghan, M. and Tatari, M. (2006a), “The use of Adomian decomposition method for solving problems in calculus of variations”, Mathematical Problems in Engineering, Vol. 2006, Article ID 65379, 12 pages, doi:10.1155/MPE/2006/65379
  24. Dehghan, M. and Tatari, M., The use of the Adomian decomposition method for solving a parabolic equation with temperature overspecification, Physica Scripta, 2006, Vol. 73, No. 3, pp. 240--245.
  25. El-Sayed, A.M.A. and Gaber, M. (2006), The Adomian decomposition method for solving partial differential equations of fractal order in finite domains, Physics Letters A, 2006, Vol. 359, No. 3, pp. 175--182. https://doi.org/10.1016/j.physleta.2006.06.024
  26. Elshehawey, E.F., Eldabe, N.T., Elghazy, E.M., and Ebaid, A., “Peristaltic transport in an asymmetric channel through a porous medium”, Applied Mathematics and Computation, 2006, Vol. 182, No. 1, pp. 140--150.
  27. El-Wakil, S.A., Abdou, M.A., and Elhanbaly, A., “Adomian decomposition method for solving the diffusion-convection-reaction equations”, Applied Mathematics and Computation, 2006, Vol. 177, No. 2, pp. 729--736.
  28. Fakharian, A., Beheshti, M.T.H. and Najafi, M. (2006), A new algorithm for solving Riccati equation using Adomian decomposition method, in Proceedings of the 9th World Scientific and Engineering Academy and Society (WSEAS) International Conference on Applied Mathematics, Istanbul, Turk ey, May 27-29, 2006, pp. 74--77.
  29. Gorguis, A. (2006), “A comparison between Cole-Hopf transformation and the decomposition method for solving Burgers’ equations”, Applied Mathematics and Computation, 2006, Vol. 173, No. 1, pp. 126--136.
  30. Grzymkowski, R., Pleszczyński, M. and Słota, D. (2006a), “The two-phase Stefan problem solved by the Adomian decomposition method”, in Hamza, M.H. (Ed.), Proceedings of the 15th IASTED International Conference on Applied Simulation and Modelling (ASM 2006), June 26-28, 2006, Rhodes, Greece, Acta Press, Calgary, pp. 511-6.
  31. Grzymkowski, R., Pleszczyński, M. and Słota, D. (2006b), “Comparing the Adomian decomposition method and the Runge-Kutta method for solutions of the Stefan problem”, International Journal of Computer Mathematics, 2006, Vol. 83 No. 4, pp. 409--417.
  32. Grzymkowski, R. and Słota, D. (2006), “One-phase inverse Stefan problem solved by Adomian decomposition method”, Computers and Mathematics with Applications, 2006, Vol. 51, No. 1, pp. 33--40.
  33. Hashim, I. (2006a), “Comparing numerical methods for the solutions of two-dimensional diffusion with an integral condition”, Applied Mathematics and Computation, 2006, Vol. 181 No. 2, pp. 880-5.
  34. Hashim, I., “Adomian decomposition method for solving BVPs for fourth-order integro-differential equations”, Journal of Computational and Applied Mathematics, 2006, Vol. 193, No. 2, pp. 658--664.
  35. Hashim, I. (2006c), “Comments on ‘a new algorithm for solving classical Blasius equation’ by L. Wang”, Applied Mathematics and Computation, 2006, Vol. 176, No. 2, pp. 700-3.
  36. Hashim, I., Noorani, M.S.M., Ahmad, R., Bakar, S.A., Ismail, E.S., and Zakaria, A.M., Accuracy of the Adomian decomposition method applied to the Lorenz system, Chaos, Solitons and Fractals, 2006, Vol. 28, No. 5, pp. 1149--1158. doi: 10.1016/j.chaos.2005.08.135
  37. Hashim, I., Noorani, M.S.M. and Al-Hadidi, M.R.S. (2006), “Solving the generalized Burgers-Huxley equation using the Adomian decomposition method”, Mathematical and Computer Modelling, Vol. 43 Nos 11/12, pp. 1404- 11.
  38. Hashim, I., Noorani, M.S.M., and Batiha, B., “A note on the Adomian decomposition method for the generalized Huxley equation”, Applied Mathematics and Computation, 2006, Vol. 181, No. 2, pp. 1439--1445.
  39. Helal, M.A. and Mehanna, M.S, A comparison between two different methods for solving KdV-Burgers equation, Chaos, Solitons and Fractals, 2006, Vol. 28, No. 2, pp. 320--326.
  40. Hosseini, M.M. (2006a), “Adomian decomposition method for solution of nonlinear differential algebraic equations”, Applied Mathematics and Computation, Vol. 181 No. 2, pp. 1737--1744.
  41. Hosseini, M.M., “Adomian decomposition method with Chebyshev polynomials”, Applied Mathematics and Computation, 2006, Vol. 175, No. 2, pp. 1685--1693.
  42. Hosseini, M.M. and Nasabzadeh, H. (2006), “On the convergence of Adomian decomposition method”, Applied Mathematics and Computation, 2006, Vol. 182, No. 1, pp. 536--543.
  43. Hou, B.-L., Sun, Y.-P., Applying mechanization for solving nonlinear boundary value problem of ordinary differential equation in reaction engineering, Computers and Applied Chemistry, 2006, 23 (3), 255-259. (in Chinese)
  44. Jafari, H. and Daftardar-Gejji, V. (2006a), Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method, Applied Mathematics and Computation, 2006, Vol. 180, No. 2, pp. 700--706. https://doi.org/10.1016/j.amc.2006.01.007
  45. Jafari, H. and Daftardar-Gejji, V. (2006b), Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition, Applied Mathematics and Computation, 2006, Vol. 180, No. 2, pp. 488--497. https://doi.org/10.1016/j.amc.2005.12.031
  46. Jafari, H. and Daftardar-Gejji, V. (2006c), Solving a system of nonlinear fractional differential equations using Adomian decomposition, Journal of Computational and Applied Mathematics, 2006, Vol. 196, No. 2, pp. 644--651. https://doi.org/10.1016/j.cam.2005.10.017
  47. Jafari, H. and Daftardar-Gejji, V. (2006d), “Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations”, Applied Mathematics and Computation, 2006, Vol. 181, No. 1, pp. 598--608.
  48. Lai, X.-J., Zhang, J.-F., Luo, J.-F., Adomian Decomposition Method for approximating the solution of the high-order dispersive cubic-quintic nonlinear Schrödinger equation, Zeitschrift für Naturforschung A, 2006, Vol. 61A, pp. 205--215.
  49. Lesnic, D., Blow-up solutions obtained using the decomposition method, Chaos, Solitons and Fractals, Vol. 28, (2006) 776--787.
  50. Lesnic, D. (2006a), “Blow-up solutions obtained using the decomposition method”, Chaos, Solitons and Fractals, 2006, Vol. 28 No. 3, pp. 776-87.
  51. Lesnic, D. (2006b), “The decomposition method for initial value problems”, Applied Mathematics and Computation, 2006, Vol. 181 No. 1, pp. 206-13.
  52. Lesnic, D., The decomposition method for linear, one-dimensional, time-dependent partial differential equations, International Journal of Mathematics and Mathematical Sciences, 2006, Vol. 2006, Article ID 42389, 29 pages, doi:10.1155/IJMMS/2006/42389
  53. Luo, X.-G., Wu, Q.-B. and Zhang, B.-Q. (2006), “Revisit on partial solutions in the Adomian decomposition method: solving heat and wave equations”, Journal of Mathematical Analysis and Applications, Vol. 321 No. 1, pp. 353--363.
  54. Mahmood, A.S., Casasús, L. and Al-Hayani, W. (2006), “Analysis of resonant oscillators with the Adomian decomposition method”, Physics Letters A, 2006, Vol. 357 Nos 4/5, pp. 306--313. doi: 10.1016/j.physleta.2006.04.071
  55. Momani, S. (2006), “A numerical scheme for the solution of multi-order fractional differential equations”, Applied Mathematics and Computation, 2006, Vol. 182 No. 1, pp. 761-70.
  56. Momani, S., Moadi, K. and Noor, M.A. (2006), “Decomposition method for solving a system of fourth-order obstacle boundary value problems”, Applied Mathematics and Computation, Vol. 175 No. 2, pp. 923-31.
  57. Momani, S. and Noor, M.A. (2006), “Numerical methods for fourth-order fractional integro-differential equations”, Applied Mathematics and Computation, Vol. 182 No. 1, pp. 754-60.
  58. Momani, S. and Shawagfeh, N. (2006), “Decomposition method for solving fractional Riccati differential equations”, Applied Mathematics and Computation, Vol. 182 No. 2, pp. 1083--1092.
  59. Noor, N.F.M., Hashim, I., Noorani, M.S.M., A Note On The Accuracy Of The Adomian Decomposition Method Applied To The Chaotic Lorenz System, Proceedings of the 2nd IMT-GT regional Conference on Mathematics, Statistics and Applications, University saint Malaysia, Penang, June 13--15, 2006.
  60. Pourdarvish, A. (2006), “A reliable symbolic implementation of algorithm for calculating Adomian polynomials”, Applied Mathematics and Computation, 2006, Vol. 172 No. 1, pp. 545--550.
  61. Ray, S.S. (2006), “A numerical solution of the coupled sine-Gordon equation using the modified decomposition method”, Applied Mathematics and Computation, 2006, Vol. 175 No. 2, pp. 1046-54.
  62. Ray, S.S., and Bera, R.K., “Analytical solution of a fractional diffusion equation by Adomian decomposition method,” Applied Mathematics and Computation, 2006, vol. 174, no. 1, pp. 329–336, 2006.
  63. Ray, S.S., Chaudhuri, K.S. and Bera, R.K. (2006), “Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method”, Applied Mathematics and Computation, 2006, Vol. 182 No. 1, pp. 544--552.
  64. Serrano, S.E. (2006), “Development and verification of an analytical solution for forecasting nonlinear kinematic flood waves”, Journal of Hydrologic Engineering, Vol. 11 No. 4, pp. 347--353.
  65. Srivastava, K., Serrano, S.E. and Workman, S.R. (2006), “Stochastic modeling of transient stream-aquifer interaction with the nonlinear Boussinesq equation”, Journal of Hydrology, Vol. 328 Nos 3/4, pp. 538--547.
  66. Tatari, M. and Dehghan, M. (2006), “The use of the Adomian decomposition method for solving multipoint boundary value problems”, Physica Scripta, 2006, Vol. 73 No. 6, doi:10.1088/0031-8949/73/6/023.
  67. Tatari, M., Dehghan, M. and Razzaghi, M. (2006), “Determination of a time-dependent parameter in a one- dimensional quasi-linear parabolic equation with temperature overspecification”, International Journal of Computer Mathematics, Vol. 83 No. 12, pp. 905-13.
  68. Wazwaz, A.-M. (2006a), A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations, Applied Mathematics and Computation, 2006, Vol. 181 No. 2, pp. 1703---1712. https://doi.org/10.1016/j.amc.2006.03.023
  69. Wazwaz, A.-M. (2006b), Padé approximants and Adomian decomposition method for solving the Flierl- Petviashivili equation and its variants, Applied Mathematics and Computation, 2006, Vol. 182 No. 2, pp. 1812--1818. https://doi.org/10.1016/j.amc.2006.06.018
  70. Wazwaz, A.-M. (2006c), The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain, Applied Mathematics and Computation, 2006, Vol. 177 No. 2, pp. 737--744. https://doi.org/10.1016/j.amc.2005.09.102
  71. Wazwaz, A.-M., The modified decomposition method for analytic treatment of differential equations, Applied Mathematics and Computation, 2006, Volume 173, Issue 1, 1 February 2006, Pages 165--176; https://doi.org/10.1016/j.amc.2005.02.048
  72. Yusufoğlu, E. (2006), Numerical solution of Duffing equation by the Laplace decomposition algorithm, Applied Mathematics and Computation, 2006, Vol. 177, No. 2, pp. 572--580. https://doi.org/10.1016/j.amc.2005.07.072
  73. Zhang, B.-Q., Luo, X.-G. and Wu, Q.-B. (2006), The restrictions and improvement of the Adomian decomposition method, Applied Mathematics and Computation, 2006, Vol. 177 No. 1, pp. 99-104. https://doi.org/10.1016/j.amc.2005.10.034
  74. Zhang, B.-Q., Wu, Q.-B. and Luo, X.-G. (2006), Experimentation with two-step Adomian decomposition method to solve evolution models, Applied Mathematics and Computation, 2006, Vol. 175 No. 2, pp. 1495-502. https://doi.org/10.1016/j.amc.2005.08.029
  75. Zhang, Y. and Xue, D. (2006), “Dynamical simulation analysis based on time fractional transmission line model”, in 7th International Symposium on Antennas, Propagation and EM Theory (ISAPE ’06), October 26-29, 2006, IEEE, doi:10.1109/ISAPE.2006.353525.

Reference List for ADM, 2007

  1. Abassy, T.A., El-Tawil, M.A., Saleh, H.K., The solution of Burgers’ and good Boussinesq equations using ADM–Padé technique, Chaos, Solitons and Fractals, 2007, Vol. 32, No. ?, pp. 1008--1026.
  2. Abbasbandy, S., “A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method”, Chaos, Solitons & Fractals, 2007, Vol. 31, No. 1, pp. 257--260.
  3. Alabdullatif, M., Abdusalam, H.A. and Fahmy, E.S. (2007), Adomian decomposition method for nonlinear reaction diffusion system of Lotka-Volterra type, International Mathematical Forum, 2007, Vol. 2, No. 2, pp. 87--96.
  4. Al-Khawaja, U. and Al-Khaled, K., “Error control in Adomian’s decomposition method applied to the time-dependent Gross-Pitaevskii equation”, International Journal of Computer Mathematics, 2007, Vol. 84, No. 1, pp. 81--87.
  5. Allan, F.M., Derivation of the Adomian decomposition methodusing the homotopy analysis method, Applied Mathematics and Computation, 2007, Vol. 190, pp. 6--14.
  6. Basto, M., Semiao, V., and Calheiros, F.L., Numerical study of modified Adomian’s method applied to Burgers equation, Journal of Computational and Applied Mathematics, 2007, Vol. 206, No. 2, pp. 927--949.
  7. Behiry, S.H., Hashish, H., El-Kalla, I.L., and Elsaid, A., “A new algorithm for the decomposition solution of nonlinear differential equations”, Computers and Mathematics with Applications, 2007, Vol. 54, No. 4, pp. 459--466.
  8. Biazar, J. and Ayati, Z. (2007), An approximation to the solution of the Brusselator system by Adomian decomposition method and comparing the results with Runge-Kutta method, International Journal of Contemporary Mathematical Sciences, 2007, Vol. 2, No. 20, pp. 983--989.
  9. Biazar, J. and Ebrahimi, H. (2007), An approximation to the solution of telegraph equation by Adomian decomposition method, International Mathematical Forum, 2007, Vol. 2, No. 45, pp. 2231--2236.
  10. Biazar, J. and Pourabd, M. (2007), A Maple program for solving systems of linear and nonlinear integral equations by Adomian decomposition method, International Journal of Contemporary Mathematical Sciences, 2007, Vol. 2, No. 29, pp. 1425--1432.
  11. Biazar, J. and Shafiof, S.M. (2007), A simple algorithm for calculating Adomian polynomials, International Journal of Contemporary Mathematical Sciences, 2007, Vol. 2, No. 20, pp. 975--982.
  12. Boonyapibanwong, S. and Koonprasert, S. (2007), “Analytical solutions of a model of tsunami run-up on the coast using Adomian decomposition method”, in The 11th Annual National Symposium on Computational Science and Engineering (ANSCSE11), Prince of Songk la University, Phuk et, Thailand, March 28-30, 2007.
  13. Cafagna, D. and Grassi, G., “Chaotic and hyperchaotic dynamics in Chua’s circuits: the Adomian decomposition approach”, 2007 IEEE International Conference on Electro/Information Technology, May 17-20, 2007, IEEE, pp. 79-84, doi:10.1109/EIT.2007.4374456.
  14. Cafagna, D. and Grassi, G., “Chaotic dynamics of the fractional Chua’s circuit: time-domain analysis via decomposition method”, in 18th European Conference on Circuit Theory and Design (ECCTD 2007), IEEE, August 27-30, 2007, pp. 1030-3, doi:10.1109/ECCTD.2007.4529775.
  15. Cafagna, D. and Grassi, G., "Decomposition method for studying smooth Chua's equation with application to hyperchaotic multiscroll attractors," International Journal of Bifurcation and Chaos, 2007, Vol. 17, No. 01, pp. 209--226.
  16. Chowdhury, M.S.H., Hashim, I. and Mawa, S. (2007), “Solution of prey-predator problem by multistage decomposition method”, in Atan, K.A.M., Krishnarajah, I.S. and Isamidin, R. (Eds.), International Conference on Mathematical Biology 2007 (ICMB07), Putrajaya, Malaysia, September 4-6, 2007, AIP Conference Proceedings, Vol. 971, Springer, Berlin, pp. 219-23.
  17. Daftardar-Gejji, V. and Jafari, H. (2007), “Solving a multi-order fractional differential equation using Adomian decomposition”, Applied Mathematics and Computation, 2007, Vol. 189, No. 1, pp. 541--548.
  18. Darvishi, M.T. and Barati, A., “A third-order Newton-type method to solve systems of nonlinear equations”, Applied Mathematics and Computation, 2007, Vol. 187, No. 2, pp. 630--635.
  19. Darvishi, M.T. and Barati, A., “Super cubic iterative methods to solve systems of nonlinear equations”, Applied Mathematics and Computation, 2007, Vol. 188, No. 2, pp. 1678--1685.
  20. Dehghan, M., Hamidi, A. and Shakourifar, M. (2007), “The solution of coupled Burgers’ equations using Adomian-Padé technique”, Applied Mathematics and Computation, 2007, Vol. 189, No. 2, pp. 1034--1047.
  21. Duan, J.-S., “Solution of system of fractional differential equations by Adomian decomposition method”, Applied Mathematics Journal of Chinese Universities Series B, 2007, Vol. 22, No. 1, pp. 7--12.
  22. Eldabe, N.T., Elghazy, E.M. and Ebaid, A. (2007), “Closed form solution to a second order boundary value problem and its application in fluid mechanics”, Physics Letters A, Vol. 363 No. 4, pp. 257-9.
  23. El-Gamel, M. (2007), “A comparison between Sinc-Galerkin method and the modified decomposition method for solving two-point Boundary value problem”, Journal of Computational Physics, 2007, Vol. 223(1), pp. 369–383.
  24. El-Gamel, M. (2007), “Comparison of the solutions obtained by Adomian decomposition and wavelet-Galerkin methods of boundary-value problems”, Applied Mathematics and Computation, Vol. 186 No. 1, pp. 652-64.
  25. El-Kalla, I.L. (2007), Error analysis of Adomian series solution to a class of nonlinear differential equations, Applied Mathematics E-Notes, 2007, Vol. 7, pp. 214--221.
  26. Ganji, D.D., Nourollahi, M., Rostamian, M., A comparison of variational iteration method with Adomian’s Decomposition Method in some highly nonlinear equations, International Journal of Science and Technology, 2007, 2(2):179–188.
  27. Ghosh, S., Roy, A. and Roy, D. (2007), An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, Computer Methods in Applied Mechanics and Engineering, 2007, Vol. 196, Nos 4/6, pp. 1133--1153.
  28. Gu, H. and Li, Z. (2007), “A modified Adomian method for system of nonlinear differential equations”, Applied Mathematics and Computation, 2007, Vol. 187, No. 2, pp. 748--755.
  29. Hashim, I, Noorani, M.S.M., Ahmad, R., Bakar, S.A., Ismail, E.S., Zakaria, A.M., Accuracy of the Adomian decomposition methodapplied to the Lorenz system, Chaos Solitons & Fractals, 2006, Vol. 28, pp. 1149--1158.
  30. Helal, M.A. and Mehanna, M.S. (2007a), A comparative study between two different methods for solving the general Korteweg-de Vries equation (gKdV), Chaos, Solitons and Fractals, 2007, Vol. 33, No. 3, pp. 725--739.
  31. Helal, M.A. and Mehanna, M.S., The tanh method and Adomian decomposition method for solving the foam drainage equation, Applied Mathematics and Computation, 2007, Vol. 190, No. 1, pp. 599--609.
  32. Hosseini, M.M. and Nasabzadeh, H. (2007), Modified Adomian decomposition method for specific second order ordinary differential equations, Applied Mathematics and Computation, 2007, Vol. 186 No. 1, pp. 117--123. https://doi.org/10.1016/j.amc.2006.07.094
  33. Jang, B. (2007), “Exact solutions to one dimensional non-homogeneous parabolic problems by the homogeneous Adomian decomposition method”, Applied Mathematics and Computation, Vol. 186 No. 2, pp. 969-79.
  34. Javidi, M. and Golbabai, A. (2007), Adomian decomposition method for approximating the solution of the parabolic equations, Applied Mathematical Sciences, 2007, Vol. 1, No. 5, pp. 219--225.
  35. Javadi, Sh., Davari, A. and Babolian, E. (2007), “Numerical implementation of the Adomian decomposition method for nonlinear Volterra integral equations of the second kind”, International Journal of Computer Mathematics, Vol. 84 No. 1, pp. 75-9.
  36. Kamdem, J. Sadefo and Qiao, Z. (2007), “Decomposition method for the Camassa-Holm equation”, Chaos, Solitons and Fractals, Vol. 31 No. 2, pp. 437-47.
  37. Kechil, S.A. and Hashim, I. (2007a), “Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method”, Physics Letters A, 2007, Vol. 363, Nos 1/2, pp. 110--114. https://doi.org/10.1016/j.physleta.2006.11.054
  38. Kechil, S.A. and Hashim, I., “Series solution for unsteady boundary-layer flows due to impulsively stretching plate”, Chinese Physics Letters, 2007, Vol. 24, No. 1, pp. 139--42. doi: 10.1088/0256-307X/24/1/038
  39. Kechil, S.A., Hashim, I., and Jiet, S.S., “Approximate analytical solutions for a class of laminar boundary-layer equations”, Chinese Physics Letters, 2007, Vol. 24, No. 7, pp. 1981--1984.
  40. Lesnic, D. (2007a), “A nonlinear reaction-diffusion process using the Adomian decomposition method”, International Communications in Heat and Mass Transfer, Vol. 34 No. 2, pp. 129-35.
  41. Lesnic, D. (2007b), “A reliable technique for solving third-order dispersion equations”, Kybernetes, Vol. 36 Nos 5/6, pp. 697-708.
  42. Lesnic, D., The decomposition method for Cauchy reaction-diffusion problems, Applied Mathematics Letters, 2007, Vol. 20, No. 4, pp. 412--418.
  43. Lesnic, D. and Attili, B.S. (2007), “An efficient method for sixth-order Sturm-Liouville problems”, International Journal of Science and Technology, 2007, Vol. 2, No. 2, pp. 109--114.
  44. Machado, J.M. and Shiyou, Y. (2007), “The Adomian’s decomposition method in electrostatics”, in Proceedings of the 16th Conference on the Computation of Electromagnetic Fields (COMPUMAG 2007), Rheinisch- Westfälische Technische Hochschule (RWTH), Aachen, Germany, June 24-28, 2007, Informationstechnische Gesellschaft im VDE.
  45. Makinde, O.D. (2007a), “Solving ratio-dependent predator-prey system with constant effort harvesting using Adomian decomposition method”, Applied Mathematics and Computation, 2007, Vol. 186 No. 1, pp. 17-22.
  46. Makinde, O.D. (2007b), “Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy”, Applied Mathematics and Computation, 2007, Vol. 184 No. 2, pp. 842-8.
  47. Tatari, M. Dehghan, M. Razzaghi, M., Application of Adomain decomposition methodfor the Fokker-Planck equation, Mathematics and Computer Modelling (2007) 639--650.
  48. Makinde, O.D., Olajuwon, B.I. and Gbolagade, A.W. (2007), “Adomian decomposition approach to a boundary layer flow with thermal radiation past a moving vertical porous plate”, International Journal of Applied Mathematics and Mechanics, 2007, Vol. 3 No. 3, pp. 62-70.
  49. Mamaloukas, C. (2007), “An approximate solution of Burger’s equation using Adomian’s decomposition method”, International Journal of Pure and Applied Mathematics, 2007, Vol. 39 No. 2, pp. 203-11.
  50. Memarbashi, R. (2007), “Variational problems with moving boundaries using decomposition method”, Mathematical Problems in Engineering, Vol. 2007, Article ID 10120, 11 pages, doi:10.1155/2007/10120.
  51. Meštrović, M. (2007), “The modified decomposition method for eighth-order boundary value problems”, Applied Mathematics and Computation, 2007, Vol. 188 No. 2, pp. 1437-44.
  52. Momani, S. (2007), “A decomposition method for solving unsteady convection-diffusion problems”, Turk ish Journal of Mathematics, 2007, Vol. 31, pp. 1-10.
  53. Momoniat, E., Selway, T.A. and Jina, K. (2007), “Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow”, Nonlinear Analysis: Theory, Methods and Applications, 2007, Vol. 66 No. 10, pp. 2315--2324.
  54. Noorani, M.S.M., Hashim, I., Ahmad, R., Bakar, S.A., Ismail, E.S. and Zakaria, A.M. (2007), “Comparing numerical methods for the solutions of the Chen system”, Chaos, Solitons and Fractals, 2007, Vol. 32 No. 4, pp. 1296--1304.
  55. Rahman, M.A., Mustafiz, S., Biazar, J., Koksal, M. and Islam, M.R. (2007), “Investigation of a novel perforation technique in petroleum wells – perforation by drilling”, Journal of the Frank lin Institute, Vol. 344 No. 5, pp. 777--789.
  56. Ray, S.S. (2007), Solution of the coupled Klein-Gordon Schrödinger equation using the modified decomposition method, International Journal of Nonlinear Science, 2007, Vol. 4 No. 3, pp. 227-34,
  57. Ruan, J., Lu, Z., A modified algorithm for the Adomian decomposition method with applications to Lotka–Volterra systems, Mathematical and Computer Modelling, 2007, Volume 46, Issues 9–10, November 2007, Pages 1214-1224; https://doi.org/10.1016/j.mcm.2006.12.038
  58. Scott, K. and Sun, Y.-P. (2007), “Approximate analytical solutions for models of three-dimensional electrodes by Adomian’s decomposition method”, in Vayenas, C., White, R.E. and Gamboa-Adelco, M.E. (Eds.), Modern Aspects of Electrochemistry, No. 41, Springer, New York, NY, pp. 222-304.
  59. Serrano, S.E., Workman, S.R., Srivastava, K. and Miller-Van Cleave, B. (2007), “Models of nonlinear stream aquifer transients”, Journal of Hydrology, 2007, Vol. 336 Nos 1/2, pp. 199-205.
  60. Somali, S. and Gokmen, G. (2007), “Adomian decomposition method for nonlinear Sturm-Liouville problems”, Surveys in Mathematics and its Applications, Vol. 2, pp. 11-20.
  61. Srivastava, K. and Serrano, S.E. (2007), “Uncertainty analysis of linear and nonlinear groundwater flow in a heterogeneous aquifer”, Journal of Hydrologic Engineering, Vol. 12 No. 3, pp. 306--318.
  62. Tatari, M. and Dehghan, M. (2007), “Identifying a control function in parabolic partial differential equations from overspecified boundary data”, Computers and Mathematics with Applications, Vol. 53 No. 12, pp. 1933-42.
  63. Tatari, M., Dehghan, M. and Razzaghi, M. (2007), Application of the Adomian decomposition method for the Fokker-Planck equation, Mathematical and Computer Modelling, 2007, Vol. 45, Nos 5/6, pp. 639--650.
  64. Wazwaz, A.-M. (2007), A comparison between the variational iteration method and Adomian decomposition method, Journal of Computational and Applied Mathematics, 2007, Vol. 207 No. 1, pp. 129--136. https://doi.org/10.1016/j.cam.2006.07.018
  65. Wu, L., Zong, F.D. and Zhang, J.F. (2007), “Adomian decomposition method for nonlinear differential-difference equation”, Communications in Theoretical Physics, Vol. 48 No. 6, pp. 983-6.
  66. Yahaya, F., Hashim, I., Ismail, E.S. and Zulkifle, A.K. (2007), “Direct solutions of nth-order initial value problems in decomposition series”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8 No. 3, pp. 385-92.

Reference List for ADM, 2008

  1. Abdulaziz, O., Noor, N.F.M., Hashim, I., and Noorani, M.S.M., “Further accuracy tests on Adomian decomposition method for chaotic systems”, Chaos, Solitons and Fractals, 2008, Vol. 36, No. 5, pp. 1405--1411.
  2. Adegboyegun B.J. and Ibijola E.A. and Adegboyegun B.J., On the Theory and Application of Adomian Decomposition Method for Numerical Solution of Second other Ordinary Differential Equation. The Pacific Journal of Science and Technology, Volume 9 (2): 357 -362 November 2008.
  3. Agusto, F.B., Adomian Decomposition Method for the Solution ofOptimal Control of Waste Water Model, Mathematical Sciences, 2008, Vol. 2, No. 2, pp. 159--180.
  4. Al-Dosary, K.I., Al-Jubouri, N.K., and Abdullah, H.K., “On the solution of Abel differential equation by Adomian decomposition method”, Applied Mathematical Sciences, 2008, Vol. 2, No. 43, 2105--2118.
  5. Al-Humedi, H.O. and Ali, A.H., “Application of Adomian decomposition method to solve Fisher’s equation”, Journal of Basrah Researches (Sciences), 2008, Vol. 35, pp. 23--32.
  6. Ali, A.H. and Al-Saif, A.S.J., “Adomian decomposition method for solving some models of nonlinear partial differential equations”, Basrah Journal of Science (A), 2008, Vol. 26, No. 1, pp. 1--11.
  7. Al-Sawalha, M.M., Noorani, M.S.M., Hashim, I., Numerical experiments on the hyperchaotic Chen system by the Adomian decomposition method, International Journal of Computational Methods, 2008, Vol. 5, No. 3, pp. 1–10.
  8. Amani, A.R. and Sadeghi, J. (2008), Adomian decomposition method and two coupled scalar fields, Balan, V. (Ed.), in Balk an Society of Geometers (BSG) Proceedings of the 15th International Conference on “Differential Geometry and Dynamical Systems” (DGDS-2007), Bucharest, Romania, October 5-7, 2007, Geometry Balkan Press, Bucharest, Romania, pp. 11--18.
  9. Aslanov, A. and Abu-Alshaikh, I., “Further developments to the decomposition method for solving singular initial-value problems”, Mathematical and Computer Modelling, 2008, Vol. 48, Nos 5/6, pp. 700--711.
  10. Babajee, D.K.R., Dauhoo, M.Z., Darvishi, M.T., and Barati, A., “A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule”, Applied Mathematics and Computation, 2008, Vol. 200, No. 1, pp. 452--458.
  11. Banerjee, A., Bhattacharya, B., and Mallik, A.K., “Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches”, International Journal of Non-Linear Mechanics, 2008, Vol. 43, No. 5, pp. 366--76.
  12. Biazar, J. and Ghazvini, H., An analytical approximation to the solution of a wave equation by a variational iteration method, Applied Mathematics Letters, 2008, Vol. 21, pp. 780–785; https://doi.org/10.1016/j.aml.2007.08.004
  13. Bratsos, A., Ehrhardt, M. and Famelis, I.Th., “A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations”, Applied Mathematics and Computation, 2008, Vol. 197, No. 1, pp. 190--205.
  14. Chang, S.H., and Chang, I.L., A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Applied Mathematics and Computation, 2008, Vol. 195, Issue 2, pp. 799--808. https://doi.org/10.1016/j.amc.2007.05.026
  15. Chen, Y. and An, H.-L. (2008), "Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives," Applied Mathematics and Computation, 2008, Vol. 200, No. 1, pp. 87--95. Available on the web.
  16. Daftardar-Gejji, V. and Bhalekar, S. (2008), “Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method”, Applied Mathematics and Computation, 2008, Vol. 202, No. 1, pp. 113--120. https://doi.org/10.1016/j.amc.2008.01.027
  17. Dahmani, Z., Mesmoudi, M.M., Bebbouchi, R., The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method, Electronic Journal of Qualitative Theory of Differential Equations, 2008, No. 30, pp. 1--10.
  18. Dehghan, M. and Shakeri, F. (2008), “The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics”, Physica Scripta, 2008, Vol. 78, No. 6, doi:10.1088/0031-8949/78/06/065004
  19. Ebaid, A., “A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method”, Physics Letters A, 2008, Vol. 372, No. 32, pp. 5321--5328.
  20. Edarh-Bossou, T., Birregah, B., A case study of an Hamilton-Jacobi equation by the Adomian decompositional method, hal-00343171￿, arXiv:0812.0582, 2008.
  21. El-Kalla, I.L., “Convergence of the Adomian method applied to a class of nonlinear integral equations”, Applied Mathematics Letters, 2008, Vol. 21, No. 4, pp. 372--376.
  22. Esmaili, Q., Ramiar, A., Alizadeh E., and Ganji, D.D., An approximation of the analytical solution of the Jeffery--Hamel flow by decomposition method, Physics Letters, A, 2008, 372, (19), 3434–3439. https://doi.org/10.1016/j.physleta.2008.02.006
  23. Fahmy, E.S., Abdusalam, H.A. and Raslan, K.R. (2008), “On the solutions of the time-delayed Burgers equation”, Nonlinear Analysis: Theory, Methods and Applications, 2008, Vol. 69, No. 12, pp. 4775--4786.
  24. Fahmy, E.S., Raslan, K.R. and Abdusalam, H.A. (2008), “On the exact and numerical solution of the time-delayed Burgers equation”, International Journal of Computer Mathematics, 2008, Vol. 85, No. 11, pp. 1637--1648.
  25. Ganji, D.D., Sadeghi, E.M.M. and Rahmat, M.G. (2008), “Modified Camassa-Holm and Degasperis-Procesi equations solved by Adomian’s decomposition method and comparison with HPM and exact solutions”, Acta Applicandae Mathematicae, 2008, Vol. 104, No. 3, pp. 303--311.
  26. Garai, T., Mukhopadhyay, S. and Ghose, D. (2008), “Closed-form solution of RTPN guidance law using Adomian decomposition”, IEEE Region 10 and the Third International Conference on Industrial and Information Systems (ICIIS 2008), December 8-10, 2008, IEEE, doi:10.1109/ICIINFS.2008.4798491
  27. Gorguis, A. and Chan, W.K.B. (2008), “Heat equation and its comparative solutions”, Computers and Mathematics with Applications, 2008, Vol. 55, No. 12, pp. 2973--2980.
  28. Hasan, Y.Q. and Zhu, L.M., Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations, Surveys in Mathematics and its Applications, 2008, Vol. 3, pp. 183--193.
  29. Hsu, J.-C., Lai, H.-Y., and Chen, C.-K., Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method, Journal of Sound and Vibration, 2008, Vol. 318, Nos 4/5, pp. 965--981.
  30. Ibijola E.A. and Adegboyegun B.J., On Adomian Decompositoon Method (ADM) for Numerical Solution of Ordinary Differential Equation. Advances in Natural Applied Sciences, 2008, Vol. 2, No. 3, pp. 165 –169, 2008
  31. Jang, B., Two-point boundary value problems by the extended Adomian decomposition method, Journal of Computational and Applied Mathematics, 2008, Vol. 219, Issue 1, pp. 253--262.
  32. Jaradat, O.K. (2008), Adomian decomposition method for solving Abelian differential equations, Journal of Applied Sciences, 2008, Vol. 8, No. 10, pp. 1962--1966,
  33. Jiao, Y.-C., Dang, C., Yamamoto, Y., An extension of the decomposition method for solving nonlinear equations and its convergence, Computers and Mathematics with Applications, 2008, Vol. 55, pp. 760--775
  34. Kechil, S.A. and Hashim, I. (2008a), “Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field”, Physics Letters A, Vol. 372, No. 13, pp. 2258--2263.
  35. Kechil, S.A. and Hashim, I. (2008b), “Symbolic solution to magnetohydrodynamic Hiemenz flow in porous media”, in Kapur, D. (Ed.), 8th Asian Symposium on Computer Mathematics (ASCM 2007), Proceedings of the Revised and Invited Papers, Singapore, December 2007, Lecture Notes in Artificial Intelligence 5081 (LNAI 5081), Springer, Berlin, pp. 213--223.
  36. Kechil, S.A. and Hashim, I. (2008c), “Series solutions of boundary-layer flows in porous media with lateral mass flux”, Heat and Mass Transfer, 2008, Vol. 44, No. 10, pp. 1179--1186. https://doi.org/10.1007
  37. Lai, H.-Y., Chen, C.-K., and Hsu, J.-C., Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method, Computer Modeling in Engineering and Sciences, 2008, Vol. 34, No. 1, pp. 87--113.
  38. Lai, H.-Y., Hsu, J.-C. and Chen, C.-K. (2008), An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the Adomian decomposition method, Computers and Mathematics with Applications, 2008, Vol. 56, No. 12, pp. 3204-3220. https://doi.org/10.1016/j.camwa.2008.07.029
  39. Layeni, O.P. (2008), “Remark on modifications of Adomian decomposition method”, Applied Mathematics and Computation, Vol. 197 No. 1, pp. 167-71.
  40. Layeni, O.P. and Akinola, A.P., “Adomian decomposition approach to a filtration model”, International Journal of Nonlinear Science, 2008, Vol. 5, No. 2, pp. 158--163.
  41. Lesnic, D. (2008a), “A direct solution of a damped force vibration problem. I. Single-degree-of-freedom”, International Journal of Computational Mathematics and Numerical Simulation, Vol. 1 No. 1, pp. 113-29.
  42. Lesnic, D. (2008b), “A direct solution of a damped force vibration problem. II. Multiple-degrees-of-freedom”, International Journal of Computational Mathematics and Numerical Simulation, Vol. 1 No. 1, pp. 1-11.
  43. Lesnic, D. (2008c), “Decomposition method for Fisher’s equation with nonlinear diffusion”, International Journal of Computational Mathematics and Numerical Simulation, Vol. 1 No. 2, pp. 187-92.
  44. Lesnic, D. (2008d), “The decomposition method for nonlinear, second-order, parabolic partial differential equations”, International Journal of Computational Mathematics and Numerical Simulation, 2008, Vol. 1, No. 2, pp. 207--233.
  45. Marwat, D.N.K. and Asghar, S. (2008), “Solution of the heat equation with variable properties by two-step Adomian decomposition method”, Mathematical and Computer Modelling, Vol. 48 Nos 1/2, pp. 83-90.
  46. Mittal, R.C. and Nigam, R. (2008a), Solution of a class of singular boundary value problems, Numerical Algorithms, 2008, Vol. 47, No. 2, pp. 169--179.
  47. Mittal, R.C. and Nigam, R. (2008b), “Solution of fractional integro-differential equations by Adomian decomposition method”, International Journal of Applied Mathematics and Mechanics, Vol. 4, No. 2, pp. 87-94.
  48. Momani, S. and Jafari, H. (2008), “Numerical study of systems of fractional differential equations by using the decomposition method”, Southeast Asian (SEA) Bulletin of Mathematics, 2008, Vol. 32, pp. 721-30.
  49. Mustafiz, S., Mousavizadegan, S.H. and Islam, M.R. (2008), “Adomian decomposition of Buckley-Leverett equation with capillary effects”, Petroleum Science and Technology, Vol. 26, pp. 1796-810.
  50. Nouri, K., Garshasbi, M. and Damirchi, J. (2008), Application of Adomian decomposition method to solve a class of diffusion problem arises during MRI, Mathematical Sciences Quarterly Journal (MSQJ), Vol. 2 No. 2, pp. 207- 18
  51. Olayiwola, M.O., Gbolagade, A.W., Ayeni, R.O. and Mustapha, A.R. (2008), On the existence of solution of differential equation of fractional order, Journal of Modern Mathematics and Statistics, Vol. 2 No. 5, pp. 157--159.
  52. Rach, R., A new definition of the Adomian polynomials, Kybernetes, 2008, vol.37, pp. 910–955.
  53. Ray, S.S. (2008a), “A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends”, Applied Mathematics and Computation, Vol. 202 No. 2, pp. 544--549.
  54. Ray, S.S. (2008b), “An application of the modified decomposition method for the solution of the coupled Klein- Gordon-Schrödinger equation”, Communications in Nonlinear Science and Numerical Simulation, Vol. 13 No. 7, pp. 1311--1317.
  55. Ray, S.S., Chaudhuri, K.S. and Bera, R.K. (2008), “Application of modified decomposition method for the analytical solution of space fractional diffusion equation”, Applied Mathematics and Computation, 2008, Vol. 196 No. 1, pp. 294-302.
  56. Serrano, S.E. and Workman, S.R. (2008), “Experimental verification of models of nonlinear stream aquifer transients”, Journal of Hydrologic Engineering, 2008, Vol. 13 No. 12, pp. 1119--1124
  57. Soliman, A.A. and Abdou, M.A. (2008), “The decomposition method for solving the coupled modified KdV equations”, Mathematical and Computer Modelling, 2008, Vol. 47, Nos 9/10, pp. 1035--1041.
  58. Su, X.-H., Zheng, L.-C. and Jiang, F. (2008), “Approximate analytical solutions and approximate value of skin friction coefficient for boundary layer of power law fluids”, Applied Mathematics and Mechanics (English Edition), Vol. 29 No. 9, pp. 1215--1220.
  59. Waewcharoen, S., Boonyapibanwong, S. and Koonprasert, S. (2008), “Application of 2D-nonlinear shallow water model of tsunami by using Adomian decomposition method”, in Simos, T.E., Psihoyios, G. and Tsitouras, Ch. (Eds.), International Conference on Numerical Analysis and Applied Mathematics 2008, Psalidi, Kos, Greece, September 16-20, 2008, AIP Conference Proceedings, Vol. 1048, Springer, Berlin, pp. 580--584.
  60. Yang, P., Chen, Y. and Li, Z. (2008), “Adomian decomposition method and Padé approximants for solving the Blaszak-Marciniak lattice”, Chinese Physics B, Vol. 17 No. 11, pp. 3953-64.
  61. Yang, Y.-T., Chien, S.-K. and Chen, C.-K. (2008), “A double decomposition method for solving the periodic base temperature in convective longitudinal fins”, Energy Conversion and Management, Vol. 49 No. 10, pp. 2910--2916.

Reference List for ADM, 2009

  1. Abdelwahid, F. and Rach, R., “On the foundation of the Adomian decomposition method”, Journal of Natural and Physical Sciences, 2009, Vol. 23, Nos 1/2, pp. 13--29.
  2. Achouri, T. and Omrani, K., “Numerical solutions for the damped generalized regularized long-wave equation with a variable coefficient by Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 5, pp. 2025--2033.
  3. Al-Bayati, A.Y., Al-Sawoor, A.J. and Samarji, M.A., “A multistage Adomian decomposition method for solving the autonomous van der Pol system”, Australian Journal of Basic and Applied Sciences, 2009, Vol. 3, No. 4, pp. 4397--4407.
  4. Ali, A.H. and Al-Saif, A.S.J., Adomian decomposition method for so lving some models of nonlinear partial differential equations, Basrah Journal of Scienec (A), 2008, Vol. 26, No. 1, pp. 1--11.
  5. Alizadeh, E., Sedighi, K., Farhadi, M., and Ebrahimi-Kebria, H.R., Analytical approximate solution of the cooling problem by Adomian decomposition method, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 2, pp. 462--472. https://doi.org/10.1016/j.cnsns.2007.09.008
  6. Al-Sawalha, M.M., Noorani, M.S.M., Hashim, I., On accuracy of Adomian decomposition method forhyperchaotic Ro¨ssler system, Chaos, Solitons and Fractals, 2009, Vol. 40, pp. 1801–180; doi:10.1016/j.chaos.2007.09.062
  7. Arenas, A.J., González-Parra, G., Jódar, L., and Villanueva, R.J., “Piecewise finite series solution of nonlinear initial value differential problem”, Applied Mathematics and Computation, 2009, Vol. 212, No. 1, pp. 209--215.
  8. Aslanov, A., “Approximate solutions of Emden-Fowler type equations”, International Journal of Computer Mathematics, 2009, Vol. 86, No. 5, pp. 807--826.
  9. Azreg-Aïnou, M., A developed new algorithm for evaluating Adomian polynomials, CMES: Computer Modeling in Engineering and Sciences, 2009, Vol. 42, No. 1, pp. 1--18.
  10. Basak, K.C., Ray, P.C. and Bera, R.K., “Solution of non-linear Klein--Gordon equation with a quadratic non-linear term by Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 3, pp. 718--723. https://doi.org/10.1016/j.cnsns.2007.09.018
  11. AL Bayati, A.Y., ALSawoor, A.J., Samarji, M.A., A multistage Adomian Decomposition Method for solving the autonomous van der Pol system, Australian Journal of Basic and Applied Sciences, 3(4): 4397-4407, 2009
  12. Bohner, M. and Zheng, Y. (2009), On analytical solutions of the Black-Scholes equation, Applied Mathematics Letters, 2009, Vol. 22, No. 3, pp. 309--313. https://doi.org/10.1016/j.aml.2008.04.002
  13. Bokhari, A.H., Mohammad, G., Mustafa, M.T. and Zaman, F.D., Adomian decomposition method for a nonlinear heat equation with temperature dependent thermal properties, Mathematical Problems in Engineering, Vol. 2009, Article ID 926086, 12 pages, doi:10.1155/2009/926086
  14. Bohner, M. and Zheng, Y., On analytical solutions of the Black-Scholes equation, Applied Mathematics Letters, 2009, Vol. 22, No. 3, pp. 309--313. https://doi.org/10.1016/j.aml.2008.04.002
  15. Bokhari, A.H., Mohammad, G., Mustafa, M.T. and Zaman, F.D., Adomian decomposition method for a nonlinear heat equation with temperature dependent thermal properties, Mathematical Problems in Engineering, Vol. 2009, Article ID 926086, 12 pages, doi:10.1155/2009/926086.
  16. Bratsos, A.G., “A note on a paper by A.G. Bratsos, M. Ehrhardt and I.Th. Famelis”, Applied Mathematics and Computation, 2009, Vol. 211, No. 1, pp. 242--245.
  17. Chowdhury, M.S.H., Hashim, I. and Mawa, S. (2009), Solution of prey-predator problem by numeric-analytic technique, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 4, pp. 1008--1012. https://doi.org/10.1016/j.cnsns.2007.11.006
  18. Cordshooli, Gh.A. and Vahidi, A.R. (2009), Phase synchronization of van der Pol--Duffing oscillators using decomposition method, Advanced Studies in Theoretical Physics, Vol. 3, No. 11, pp. 429--437.
  19. Dehghan, M. and Shakeri, F., “The numerical solution of the second Painlevé equation”, Numerical Methods for Partial Differential Equations, 2009, Vol. 25, No. 5, pp. 1238--59.
  20. Dehghan, M., Shakourifar, M. and Hamidi, A. (2009), “The solution of linear and nonlinear systems of Volterra functional equations using Adomian--Padé technique”, Chaos, Solitons and Fractals, 2009, Vol. 39, No. 5, pp. 2509--2521. https://doi.org/10.1016/j.chaos.2007.07.028
  21. El-Sayed, A.M.A., Rida, S.Z. and Arafa, A.A.M. (2009), On the solutions of time-fractional bacterial chemotaxis in a diffusion gradient chamber, International Journal of Nonlinear Science, 2009, Vol. 7, No. 4, pp. 485--492.
  22. Ganji, D.D., Safari, M., Ghayor, R., Application of He’s Variational Iteration Method and Adomian’s Decomposition Method to Sawada–Kotera–Ito Seventh-Order Equation, Acta Applicandae Mathematicae, 2009, pp. 887--897.
  23. Garai, T., Mukhopadhyay, S. and Ghose, D. (2009), “Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2009, Vol. 223 No. 3, pp. 189-99. https://doi.org/10.1243/09544100JAERO457
  24. Gharsseldien, Z.M. and Hemida, K. (2009), “New technique to avoid ‘noise terms’ on the solutions of inhomogeneous differential equations by using Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 3, pp. 685--696. https://doi.org/10.1016/j.cnsns.2007.11.018
  25. González-Parra, G., Arenas, A.J. and Jódar, L. (2009), Piecewise finite series solutions of seasonal diseases models using multistage Adomian method, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 11, pp. 3967--3977.
  26. Grzymkowski, R., Pleszczyński, M. and Słota, D., “Application of the Adomian decomposition method for solving the heat equation in the cast-mould heterogeneous domain”, Archives of Foundry Engineering, 2009, Vol. 9, No. 4, pp. 57--62.
  27. Hasan, Y.Q. and Zhu, L.M. (2009a), “Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14 No. 6, pp. 2592-6. https://doi.org/10.1016/j.cnsns.2008.09.027
  28. Hasan, Y.Q. and Zhu, L.M., A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 8, pp. 3261--3265.
  29. Hosseini, M.M. and Jafari, M. (2009a), A note on the use of Adomian decomposition method for high-order and system of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 5, pp. 1952--1957. https://doi.org/10.1016/j.cnsns.2008.04.014
  30. Hosseini, M.M. and Jafari, M., “An efficient method for solving nonlinear singular initial value problems”, International Journal of Computer Mathematics, 2009, Vol. 86, No. 9, pp. 1657--1666. https://doi.org/10.1080/00207160801965230
  31. Hsu, J.-C., Lai, H.-Y., and Chen, C.-K., “An innovative eigenvalue problem solver for free vibration of uniform Timoshenko beams by using the Adomian modified decomposition method”, Journal of Sound and Vibration, 2009, Vol. 325, Nos 1/2, pp. 451--470.
  32. Kechil, S.A. and Hashim, I. (2009a), “Approximate analytical solution for MHD stagnation-point flow in porous media”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14. No. 4, pp. 1346--1354. https://doi.org/10.1016/j.cnsns.2008.02.007
  33. Kechil, S.A. and Hashim, I. (2009b), “Flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium”, Journal of Porous Media, 2009, Vol. 12, No. 11, pp. 1053--1063.
  34. Kiymaz, O., An Algorithm for Solving Initial Value ProblemsUsing Laplace Adomian Decomposition Method, Applied Mathematical Sciences, 2009, Vol. 3, 2009, no. 30, 1453 - 1459
  35. Kundu, B. (2009a), “Approximate analytic solution for performances of wet fins with a polynomial relationship between humidity ratio and temperature”, International Journal of Thermal Sciences, V2009, ol. 48, No. 11, pp. 2108-18.
  36. Kundu, B. (2009b), “Approximate analytical method for prediction of performance and optimum dimensions of pin fins subject to condensation of quiescent vapor”, International Journal of Refrigeration, 2009, Vol. 32, No. 7, pp. 1657- 71.
  37. Kundu, B. and Ghosh, G.K. (2009), “An approximate analytical prediction about thermal performance and optimum design of pin fins subject to condensation of saturated steam flowing under forced convection”, International Journal of Refrigeration, 2009, Vol. 32, No. 5, pp. 809--825.
  38. Li, J.L., Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations. Journal of Computational and Applied Mathematics, 2009, Vol. 228(1): 168–173
  39. Li, C. and Wang, Y. (2009), “Numerical algorithm based on Adomian decomposition for fractional differential equations”, Computers and Mathematics with Applications, Vol. 57 No. 10, pp. 1672--181.
  40. Liu, Y. (2009), Adomian decomposition method with orthogonal polynomials: Legendre polynomials, Mathematical and Computer Modelling, Vol. 49 Nos 5/6, pp. 1268---1273.
  41. Liu, Y. (2009), Adomian decomposition method with second kind Chebyshev polynomials, Proceedings of the Jangjeon Mathematical Society, 2009, Vol. 12, No. 1, pp. 57--67.
  42. Nadeem, S. and Akbar, N.S. (2009), “Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14 No. 11, pp. 3844-55.
  43. Ngarasta, N. (2009), “Solving integral equations of the first kind by decomposition method”, Kybernetes, 2009, Vol. 38 No. 5, pp. 733--743.
  44. Ngarasta, N., Rodoumta, K. and Sosso, H. (2009), “The decomposition method applied to systems of linear Volterra integral equations of the first kind”, Kybernetes, Vol. 38 Nos 3/4, pp. 606--614.
  45. Noor, N.F.M. and Hashim, I. (2009), “MHD flow and heat transfer adjacent to a permeable shrinking sheet embedded in a porous medium”, Sains Malaysiana (Universiti Kebangsaan Malaysia), Vol. 38 No. 4, pp. 559--565.
  46. Pan, P., and Zhu, Y.-G., (2009), “Comparison between Adomian double decomposition method and Adomian decomposition method”, Journal of Communication University of China (Science and Technology), 2009, Vol. 16, No. 3, pp. 15--18.
  47. Parra, G.G., Arenas, A.J., Jódar, L., Piecewise finite series solutions of seasonal diseases models using multistage Adomian method, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14, No. 11, pp. 3967--3977. doi: 10.1016/j.cnsns.2009.02.023
  48. Qin, X.-Y. and Sun, Y.-P. (2009), Approximate analytic solutions for a two-dimensional mathematical model of a packed-bed electrode using the Adomian decomposition method, Applied Mathematics and Computation, 2009, Vol. 215, No. 1, pp. 270--275.
  49. Rajaram, R. and Najafi, M. (2009), “Analytical treatment and convergence of the Adomian decomposition method for a system of coupled damped wave equations”, Applied Mathematics and Computation, Vol. 212 No. 1, pp. 72- 81.
  50. Ray, S.S. (2009), “Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14 No. 4, pp. 1295-306.
  51. Rebelo, P. (2009), “An approximate solution to solid fuel models by decomposition methods”, in III conferência nacional em mecânica dos fluidos, termodinâmica e energia Instituto Politécnico de Bragança, 17-18 de Setembro de 2009.
  52. Rebelo, P. and Miranda, A. (2009), “On the approximate solution to an initial boundary valued problem to a nonlinear diffusion equation with a non-local source”, in III conferência nacional em mecânica dos fluidos, termodinâmica e energia Instituto Politécnico de Bragança, 17-18 de Setembro de 2009.
  53. Shidfar, A. and Garshasbi, M. (2009), “A weighted algorithm based on Adomian decomposition method for solving an special class of evolution equations”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14 No. 4, pp. 1146--1151. doi: 10.1016/j.cnsns.2008.04.004
  54. Taiwo, O.A. and Odetunde, O.S. (2009), “On the solution of n-point n-th order boundary value problems by a modified decomposition method”, International Journal of Physical Sciences (Pan-African Journal Series).
  55. Tien, W.-C. and Chen, C.-K. (2009), “Adomian decomposition method by Legendre polynomials, Chaos, Solitons and Fractals, Vol. 39 No. 5, pp. 2093--2101. doi: 10.1016/j.chaos.2007.06.066
  56. Tolou, N. and Herder, J.L. (2009), A semianalytical approach to large deflections in compliant beams under point load, Mathematical Problems in Engineering, 2009, Vol. 2009, Article ID 910896, 13 pages, doi:10.1155/2009/910896.
  57. Vahidi, A.R. (2009a), “Different approaches to the solution of damped forced oscillator problem by decomposition method”, Australian Journal of Basic and Applied Sciences, Vol. 3 No. 3, pp. 2249-54.
  58. Vahidi, A.R. (2009b), “Improving the accuracy of solutions of linear and nonlinear ODEs in decomposition method”, Australian Journal of Basic and Applied Sciences, Vol. 3 No. 3, pp. 2255-61.
  59. Vahidi, A.R., Babolian, E., Cordshooli, Gh.A. and Azimzadeh, Z. (2009), “Numerical solution of Fredholm integro- differential equation by Adomian’s decomposition method”, International Journal of Mathematical Analysis, 2009, Vol. 3, No. 36, pp. 1769--1773.
  60. Vahidi, A.R., Babolian, E., Cordshooli, Gh.A. and Mirzaie, M. (2009), Restarted Adomian decomposition method to systems of nonlinear algebraic equations, Applied Mathematical Sciences, 2009, Vol. 3, No. 18, pp. 883--889.
  61. Vahidi, A.R., Babolian, E., Cordshooli, Gh.A. and Samiee, F. (2009), “Restarted Adomian’s decomposition method for Duffing’s equation”, International Journal of Mathematical Analysis, Vol. 3 No. 15, pp. 711--717.
  62. Wu, L., Xie, L.D. and Zhang, J.F. (2009), “Adomian decomposition method for nonlinear differential-difference equations”, Communications in Nonlinear Science and Numerical Simulation, 2009, Vol. 14 No. 1, pp. 12-8.
  63. Yang, P., Chen, Y. and Li, Z. (2009), “ADM-Padé technique for the nonlinear lattice equations”, Applied Mathematics and Computation, 2009, Vol. 210 No. 2, pp. 362-75.

Reference List for ADM, 2010

  1. Abassy, T.A., Improved Adomian decomposition method, Computers and Mathematics with Applications, 2010, Vol. 59, No. 1, pp. 42--54.
  2. Alharbi, A. and Fahmy, E.S., “ADM-Padé solutions for generalized Burgers and Burgers--Huxley systems with two coupled equations”, Journal of Computational and Applied Mathematics, 2010, Vol. 233, No. 8, pp. 2071--2080.
  3. Al-Humedi, H.O. and Al-Qatrany, F.L.H. (2010), Modified algorithm to compute Adomian’s polynomials for solving non-linear systems of partial differential equations, International Journal of Contemporary Mathematical Sciences, 2010, Vol. 5, No. 51, pp. 2505--2521.
  4. Azreg-Aïnou, M., “Developed Adomian method for quadratic Kaluza-Klein relativity”, Classical and Quantum Gravity, 2010, Vol. 27, No. 1, doi:10.1088/0264-9381/27/1/015012
  5. Az-Zo’bi, E.A. and Al-Khaled, K., “A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws”, Applied Mathematics and Computation, 2010, Vol. 217, No. 8, pp. 4248--4256.
  6. Behiry, S.H., Abd-Elmonem, R.A., and Gomaa, A.M., “Discrete Adomian decomposition solution of nonlinear Fredholm integral equation”, Ain Shams Engineering Journal, 2010, Vol. 1, No. 1, pp. 97--101.
  7. Betancourt, R.J., Perez, M.A.G., Barocio, E.E. and Arroy, J.L. (2010), “Analysis of inter-area oscillations in power systems using Adomian-Padé approximation method”, in 9th IEEE/IAS International Conference on Industry Applications (INDUSCON), November 8-10, 2010, doi:10.1109/INDUSCON.2010.5740043
  8. Biazar, J., Porshokuhi, M.G., and Ghanbari, B., “Extracting a general iterative method from an Adomian decomposition method and comparing it to the variational iteration method”, Computers and Mathematics with Applications, 2010, Vol. 59, No. 2, pp. 622--628.
  9. Blanco-Cocom, L.D., Ávila-Vales, E.J., “The use of the Adomian method for a SIRC influenza model”, Advances in Differential Equations and Control Processes, 2010, Vol. 5, No. 2, pp. 115--127.
  10. Çavdar, š. (2010), Application of the Adomian decomposition method to the one group neutron diffusion equation, in 5th International Ege Energy Symposium and Exhibition (IEESE-5), Pamuk k ale University, Denizli, Turkey, June 27-30, 2010.
  11. Chu, H. and Liu, Y. (2010), “The new ADM-Padé technique for the generalized Emden-Fowler equations”, Modern Physics Letters B, 2010, Vol. 24, No. 12, pp. 1237--1254.
  12. Dehghan, M., Heris, J.M., Saadatmandi, A., “Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses”, Mathematical Methods in the Applied Science, 2010, Vol. 33, No. 11, pp. 1384--1398.
  13. Dehghan, M. and Salehi, R., “A seminumeric approach for solution of the eikonal partial differential equation and its applications”, Numerical Methods for Partial Differential Equations, 2010, Vol. 26, No. 3, pp. 702--722. https://doi.org/10.1002/num.20482
  14. Dehghan, M. and Salehi, R., “Solution of a nonlinear time-delay model in biology via semi-analytical approaches,” Computer Physics Communications, vol. 181, no. 7, pp. 1255–1265, 2010.
  15. Dehghan, M. and Tatari, M. (2010), “Finding approximate solutions for a class of third-order non-linear boundary value problems via the decomposition method of Adomian”, International Journal of Computer Mathematics, 2010, Vol. 87, No. 6, pp. 1256--1263.
  16. Drăgănescu, G.E., Bereteu, L., Ercuţa, A., and Luca, G., “Anharmonic vibrations of a nano-sized oscillator with fractional damping”, Communications in Nonlinear Science and Numerical Simulation, 2010, Vol. 15, No. 4, pp. 922--926.
  17. Duan, J.-S., Recurrence triangle for Adomian polynomials, Applied Mathematics and Computation, 2010, Vol. 216, No. 4, pp. 1235--1241. https://doi.org/10.1016/j.amc.2010.02.015
  18. Duan, J.-S., An efficient algorithm for the multivariable Adomian polynomials, Applied Mathematics and Computation, 2010, Vol. 217, No. 6, pp. 2456--2467. https://doi.org/10.1016/j.amc.2010.07.046
  19. Duan, J.-S. and Guo, A.-P., Reduced polynomials and their generation in Adomian decomposition methods, Computer Modeling in Engineering and Sciences, 2010, Vol. 60 No. 2, pp. 139--150. doi: 10.3970/cmes.2010.060.139
  20. Ebadi, G. and Rashedi, S. (2010), “The extended Adomian decomposition method for fourth order boundary value problems”, Acta Universitatis Apulensis (Universitatea “1 Decembrie 1918” Alba Iulia), Vol. 22, pp. 65--78.
  21. Ebaid, A., Exact solutions for a class of nonlinear singular two-point boundary value problems – the decomposition method, Zeitschrift fŰr Naturforschung A (A Journal of Physical Sciences), 2010, Vol. 65, No. 3, pp. 145--150.
  22. Ebaid, A., “Modification of Lesnic’s approach and new analytic solutions for some nonlinear second-order boundary value problems with Dirichlet boundary conditions”, Zeitschrift für Naturforschung A (A Journal of Physical Science), 2010, Vol. 65, Issue 8-9, pp. 692--696. doi: https://doi.org/10.1515/zna-2010-8-910
  23. El-Kalla, I.L. (2010), “New results on the analytic summation of Adomian series for some classes of differential and integral equations”, Applied Mathematics and Computation, 2010, Vol. 217, No. 8, pp. 3756--3763.
  24. El-Sayed, A.M.A., Behiry, S.H,. and Raslan, W.E. (2010), “Adomian’s decomposition method for solving an intermediate fractional advection-dispersion equation”, Computers and Mathematics with Applications, 2010, Vol. 59, No. 5, pp. 1759--1765.
  25. El-Sayed, A.M.A., El-Kalla, I.L. and Ziada, E.A.A. (2010a), "Adomian solution of multidimensional nonlinear differential equations of arbitrary orders", International Journal of Applied Mathematics and Mechanics, 2010, Vol. 6, No. 4, pp. 38-52, available at: www.ijamm.bc.cityu.edu.hk/ijamm/outbox/Y2010V6N4P38C2112979.pdf
  26. El-Sayed, A.M.A., El-Kalla, I.L. and Ziada, E.A.A., “Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations”, Applied Numerical Mathematics, 2010, Vol. 60, No. 8, pp. 788--797.
  27. Fakharian, A., Beheshti, M.T.H. and Davari, A. (2010), “Solving the Hamilton-Jacobi-Bellman equation using Adomian decomposition method”, International Journal of Computer Mathematics, 2010, Vol. 87, No. 12, pp. 2769--2785.
  28. Ganji, Z.Z. and Ganji, D.D. (2010), “Analytical solution of viscous flow in porous media using ADM and comparison with the numerical Runge-Kutta method”, Transport in Porous Media, 2010, Vol. 81, No. 3, pp. 527--546.
  29. Hariharan, G., Kannan, K., A comparison of Haar wavelet and Adomain decomposition method for solving one-dimensional reaction-diffusion equations, International Journal of Applied Mathematics and Computation, 2010, Volume 2(1), pp 50–61, http://ijamc.psit.in
  30. Khan, Y., Faraz, N., and Yildirim, A., Series Solution for Unsteady Gas Equation via MLDM-Pade Technique, World Applied Sciences Journal, 2010, Vol. 10, No. 12, 1452--1456.
  31. Khuri, S.A. and Sayfy, A., “A novel approach for the solution of a class of singular boundary value problems arising in physiology”, Mathematical and Computer Modelling, 2010, Vol. 52, Nos 3/4, pp. 626--636.
  32. Koochi, A., Kazemi, A.S., Beni, Y.T., Yekrangi, A. and Abadyan, M. (2010), “Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method”, Physica E: Low- dimensional Systems and Nanostructures, Vol. 43, No. 2, pp. 625-32.
  33. Kumar, M. and Singh, N., “Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems”, Computers and Chemical Engineering, 2010, Vol. 34, No. 11, pp. 1750--1760.
  34. Li, Yunhua, Song, Z., Li, Yunze, Lang, Y. and Li, D. (2010), “Theoretical analysis and numerical simulation for the spill procedure of liquid fuel of fuel air explosive with shell”, International Journal of Non-Linear Mechanics, Vol. 45 No. 7, pp. 699-703.
  35. Makinde, O.D. and Moitsheki, R.J. (2010), “On solutions of nonlinear heat diffusion model for thermal energy storage problem”, International Journal of Physical Sciences, Vol. 5 No. 3, pp. 246-50.
  36. Mao, Q. and Pietrzko, S. (2010a), “Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method”, Journal of Sound and Vibration, Vol. 329 No. 11, pp. 2068- 82.
  37. Mao, Q. and Pietrzko, S. (2010b), “Free vibration analysis of stepped beams by using Adomian decomposition method”, Applied Mathematics and Computation, 2010, Vol. 217 No. 7, pp. 3429--3441.
  38. Mohammadi-Fakhar, V. and Momeni-Masuleh, S.H. (2010), “An approximate analytic solution of the heat conduction equation at nanoscale”, Physics Letters A, 2010, Vol. 374 No. 4, pp. 595-604.
  39. Mohyud-Din, S.T., Yildirim, A. and Hosseini, S.M.M. (2010), “Numerical comparison of methods for Hirota- Satsuma model”, Applications and Applied Mathematics: An International Journal (AAM), Vol. 5 No. 10, pp. 1554--1563.
  40. Nadeem, S. and Akbar, N.S. (2010), “Corrigendum to ‘effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of Adomian decomposition method’ (Commun. Nonlinear Sci. Numer. Simulat. 2009, Vol. 14, pp. 3844-55)”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15 No. 5, pp. 1419--1420.
  41. Nejad-Asghar, M. (2010), “Non-similar collapse of singular isothermal spherical molecular cloud cores with nonzero initial velocities”, Research in Astronomy and Astrophysics, 2010, Vol. 10 No. 12, pp. 1275--1286.
  42. Noor, N.F.M. and Hashim, I. (2010), MHD viscous flow over a linearly stretching sheet embedded in a non- Darcian porous medium, Journal of Porous Media, 2010, Vol. 13 No. 4, pp. 349--355.
  43. Noor, N.F.M., Ismoen, M. and Hashim, I. (2010), “Heat-transfer analysis of MHD flow due to a permeable shrinking sheet embedded in a porous medium with internal heat generation”, Journal of Porous Media, 2010, Vol. 13, No. 9, pp. 847--854.
  44. Noor, N.F.M., Kechil, S.A. and Hashim, I. (2010), “Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15 No. 2, pp. 144--148.
  45. Olga, F., and Zdenèk, Š. (2010), “Adomian decomposition method for certain singular initial value problems”, Aplimat – Journal of Applied Mathematics, 2010, Vol. 3 No. 2, pp. 91-8.
  46. Shakeri, F., and Dehghan, M., “Application of the decomposition method of adomian for solving the pantograph equation of order m,” Zeitschrift fur Naturforschung, 2010, vol. 65, no. 5, pp. 453–460, 2010.
  47. Rebelo, P. (2010), “On the approximate solution to an initial boundary valued problem for the Cahn-Hilliard equation”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15 No. 2, pp. 225--231.
  48. Rebelo, P. and Miranda, A. (2010), “Numerical simulation of one-dimensional pulsatile flow with a combined Fourier-Adomian method”, in Pereira, J.C.F., Sequeira, A. and Pereira, J.M.C. (Eds.), Proceedings of the Fifth European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010), Lisbon, Portugal, June 14-17, 2010, Paper No. 1208.
  49. Shakeri, F. and Dehghan, M. (2010), “Application of the decomposition method of Adomian for solving the pantograph equation of order m”, Zeitschrift fŰr Naturforschung A (Physical Sciences), 2010, Vol. 65a No. 5, pp. 453- 60.
  50. Shidfar, A. and Reihani, P. (2010), “A series solution of nonlinear injection-extraction well equation”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15 No. 9, pp. 2278--2283
  51. Siddiqui, A.M., Hameed, M., Siddiqui, B.M. and Ghori, Q.K. (2010), “Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid”, Communications in Nonlinear Science and Numerical Simulation, 2010, Vol. 15 No. 9, pp. 2388--2399.
  52. Soroush, R., Koochi, A., Kazemi, A.S., Noghrehabadi, A., Haddadpour, H. and Abadyan, M. (2010), “Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano- actuators”, Physica Scripta, Vol. 82 No. 4, 045801, 11 pp., doi:10.1088/0031-8949/82/04/045801.
  53. Sweilam, N.H. and Khader, M.M. (2010), “Approximate solutions to the nonlinear vibrations of multiwalled carbon nanotubes using Adomian decomposition method”, Applied Mathematics and Computation, Vol. 217 No. 2, pp. 495-505.
  54. Tabatabaei, K. (2010), “Solution of differential equations by Adomian decomposition method”, 2010 2nd International Conference on Computer Engineering and Technology (ICCET), April 16-18, 2010, Vol. 4, IEEE, pp. V4-553-5, doi:10.1109/ICCET.2010.5485407.
  55. Taiwo, O.A. and Odetunde, O.S. (2010), “On the numerical approximation of delay differential equations by a decomposition method”, Asian Journal of Mathematics and Statistics, Vol. 3 No. 4, pp. 237--243.
  56. Tsai, P.-Y. and Chen, C.-K. (2010), “An approximate analytic solution of the nonlinear Riccati differential equation”, Journal of the Frank lin Institute, Vol. 347 No. 10, pp. 1850-62.
  57. Wazwaz, A.-M. (2010), The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations, Applied Mathematics and Computation, 2010, Vol. 216 No. 4, pp. 1304--1309. https://doi.org/10.1016/j.amc.2010.02.023
  58. Wazwaz, A.-M. and Mehanna, M.S. (2010), The combined Laplace-Adomian method for handling singular integral equation of heat transfer, International Journal of Nonlinear Science, 2010, Vol. 10 No. 2, pp. 248--252.
  59. Wu, G.-C. and He, J.-H. (2010), Fractional Adomian decomposition method, arXiv:1006.5264v1 (Mathematical Physics)
  60. Yang, Y.-T., Chang, C.-C. and Chen, C.-K. (2010), “A double decomposition method for solving the annular hyperbolic profile fins with variable thermal conductivity”, Heat Transfer Engineering, Vol. 31 No. 14, pp. 1165--1172.
  61. Zhu, H., Shu, H. and Ding, M. (2010), Numerical solutions of two-dimensional Burgers’ equations by discrete Adomian decomposition method, Computers and Mathematics with Applications, 2010, Vol. 60 No. 3, pp. 840--848. https://doi.org/10.1016/j.camwa.2010.05.031

Reference List for ADM, 2011

  1. Abadyan, M., Beni, Y.T., and Noghrehabadi, A., Investigation of elastic boundary condition on the pull-in instability of beam-type NEMS under van der Waals attraction, Procedia Engineering, 2011, Vol. 10, pp. 1724--1729.
  2. Abdelrazec, A., and Pelinovsky, D., Convergence of the Adomian decomposition method for initial-value problems, Numerical Methods for Partial Differential Equations, 2011, Vol. 27, No. 4, 749--766, 2011. https://doi.org/10.1002/num.20549
  3. Abassy, T.A., Improved Adomian decomposition method (solving nonlinear non-homogenous initial value problem), Journal of the Franklin Institute. Engineering and Applied Mathematics, 2011, vol. 348, no. 6, pp. 1035–1051, 2011. https://doi.org/10.1016/j.jfranklin.2011.04.004
  4. Adesanya, S.O. and Ayeni, E.R.O., Existence and uniqueness result for couple stress bio-fluid flow model via Adomian decomposition method, International Journal of Nonlinear Science, 2011, Vol. 12, No. 1, pp. 16--24.
  5. Al-Hayani, W., “Adomian decomposition method with Green’s function for sixth-order boundary value problems”, Computers and Mathematics with Applications, 2011, Vol. 61, No. 6, pp. 1567--1575.
  6. Al-Kurdi, A. and Mulhem, S. (2011), Solution of twelfth order boundary value problems using Adomian decomposition method, Journal of Applied Sciences Research, 2011, Vol. 7, No. 6, pp. 922--934.
  7. Al-Mazmumy, M.A., “Adomian decomposition method for solving Goursat’s problems”, SR (Scientific Research) Applied Mathematics, 2011, Vol. 2, No. 8, pp. 975--980, doi:10.4236/am.2011.28134
  8. Bildik, N., Konuralp, A., The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 2011, Volume 7, Issue 1, pp. 65--70. https://doi.org/10.1515/IJNSNS.2006.7.1.65
  9. Beni, Y.T., Abadyan, M. and Noghrehabadi, A. (2011), “Investigation of size effect on the pull-in instability of beam-type NEMS under van der Waals attraction”, Procedia Engineering, 2011, Vol. 10, pp. 1718--1723.
  10. Beni, Y.T., Koochi, A., and Abadyan, M., “Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS”, Physica E: Low-dimensional Systems and Nanostructures, 2011, Vol. 43, No. 4, pp. 979--988.
  11. Bhanja, D. and Kundu, B., “Thermal analysis of a constructal T-shaped porous fin with radiation effects”, International Journal of Refrigeration, 2011, Vol. 34, No. 6, pp. 1483--1496.
  12. Bougoffa, L., Rach, R., and Mennouni, A., “An approximate method for solving a class of weakly-singular Volterra integro-differential equations”, Applied Mathematics and Computation, 2011, Vol. 217, No. 22, pp. 8907--8913.
  13. Bougoffa, L., Rach, R., and Mennouni, A., “A convenient technique for solving linear and nonlinear Abel integral equations by the Adomian decomposition method”, Applied Mathematics and Computation, 2011, Vol. 218, No. 5, pp. 1785--1793.
  14. Cano, J.A.S., Adomian Decomposition Method for a Class of Nonlinear Problems, International Scholarly Research Notices, ISRN Applied Mathematics Volume 2011, Article ID 709753, 10 pages http://dx.doi.org/10.5402/2011/709753
  15. Çenesiz, Y. and Kurnaz, A., “Adomian decomposition method by Gegenbauer and Jacobi polynomials”, International Journal of Computer Mathematics, 2011, Vol. 88, No. 17, pp. 3666--3676.
  16. Chen, Y., Si, X. and Shen, B. (2011), Adomian method solution for flow of a viscoelastic fluid through a porous channel with expanding or contracting walls, 2011 International Conference on Multimedia Technology (ICMT), IEEE, July 26-28, 2011, pp. 2393-6, doi:10.1109/ICMT.2011.6002441.
  17. Cheng, J.-F. and Chu, Y.-M. (2011), Solution to the linear fractional differential equation using Adomian decomposition method, Mathematical Problems in Engineering, Vol. 2011, Article ID 587068, 14 pages, doi:10.1155/2011/587068.
  18. Cheniguel, A. and Ayadi, A. (2011), Solving heat equation by the Adomian decomposition method, Proceedings of the World Congress on Engineering 2011 (WCE 2011), London, UK, July 6-8, 2011, Vol. 1.
  19. Chu, H., Zhao, Y. and Liu, Y. (2011), A MAPLE package of new ADM-Padé approximate solution for nonlinear problems, Applied Mathematics and Computation, Vol. 217, No. 17, pp. 7074--7091.
  20. Cordshooli, Gh.A. and Vahidi, A.R. (2011), Solutions of Duffing--van der Pol equation using decomposition method, Advanced Studies in Theoretical Physics, 2011. Vol. 5, No. 3, pp. 121--129.
  21. Danish, M., Kumar, Sh. and Kumar, Su., “Approximate explicit analytical expressions of friction factor for flow of Bingham fluids in smooth pipes using Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, 2011, Vol. 16, No. 1, pp. 239--251.
  22. Dehghan, M. and Salehi, R., “The use of variational iteration method and Adomian decomposition method to solve the eikonal equation and its application in the reconstruction problem”, International Journal for Numerical Methods in Biomedical Engineering, 2011, Vol. 27, No. 4, pp. 524--540.
  23. Duan, J.-S., Convenient analytic recurrence algorithms for the Adomian polynomials, Applied Mathematics and Computation, 2011, Vol. 217, No. 13, pp. 6337--6348. https://doi.org/10.1016/j.amc.2011.01.007
  24. Duan, J.-S. (2011b), “New recurrence algorithms for the nonclassic Adomian polynomials”, Computers and Mathematics with Applications, Vol. 62 No. 8, pp. 2961-77.
  25. Duan, J.-S. (2011c), “New ideas for decomposing nonlinearities in differential equations”, Applied Mathematics and Computation, 2011, Vol. 218 No. 5, pp. 1774-84.
  26. Duan, J.-S. and Guo, A.-P. (2011), “Symbolic implementation of a new, fast algorithm for the multivariable Adomian polynomials”, Proceedings of the 2011 World Congress on Engineering and Technology (CET 2011), Shanghai, China, October 28-November 2, 2011, Vol. 1, IEEE Press, Beijing, pp. 72-4.
  27. Duan, J.-S. and Rach, R. (2011a), “New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods”, Applied Mathematics and Computation, Vol. 218 No. 6, pp. 2810-28.
  28. Duan, J.-S. and Rach, R., A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Applied Mathematics and Computation, 2011, Vol. 218, No. 8, pp. 4090--4118.
  29. Duan, J.-S., Sun, J. and Temuer, C.-L., “Nonlinear fractional differential equation combining Duffing equation and van der Pol equation”, Journal of Mathematics (Wuhan University), 2011, Vol. 31, No. 1, pp. 7--10.
  30. Ebaid, A., “Approximate analytical solution of a nonlinear boundary value problem and its application in fluid mechanics”, Zeitschrift für Naturforschung A (Physical Sciences), A Journal of Physical Sciences, 2011, Vol. 66, Issue 6-7, pp. 423--426. available on the web https://doi.org/10.1515/zna-2011-6-707
  31. Ebaid, A., A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, Journal of Computational and Applied Mathematics, 2011, Vol. 235, No. 8, pp. 1914--1924.
  32. El-Kalla, I.L. (2011), “Error estimate of the series solution to a class of nonlinear fractional differential equations”, Communications in Nonlinear Science and Numerical Simulation, 2011, Vol. 16, No. 3, pp. 1408--1413.
  33. Fatoorehchi, H. and Abolghasemi, H. (2011a), “Adomian decomposition method to study mass transfer from a horizontal flat plate subject to laminar fluid flow”, AENSI (American-Eurasian Network for Scientific Information) Advances in Natural and Applied Sciences, 2011, Vol. 5, No. 1, pp. 26--33.
  34. Fatoorehchi, H. and Abolghasemi, H. (2011b), “On calculation of Adomian polynomials by MATLAB”, Journal of Applied Computer Science and Mathematics (“Stefan cel Mare” University of Suceava), 2011, Vol. 11, No. 5, pp. 85--88.
  35. Ganji, D.D., Sheikholeslami, M. and Ashorynejad, H.R. (2011), Analytical approximate solution of nonlinear differential equation governing Jeffery-Hamel flow with high magnetic field by Adomian decomposition method, ISRN (International Scholarly Research Network ) Mathematical Analysis, Vol. 2011, Article ID 937830, 16 pages, doi:10.5402/2011/937830
  36. Ganji, D.D., Safari, M., Ghayor, R., Application of He’s Variational Iteration Method and Adomian’s Decomposition Method to Sawada–Kotera–Ito Seventh-Order Equation, Numerical Methods for Partial Differential Equations, 11 April 2011, https://doi.org/10.1002/num.20559
  37. Geng, F. and Cui, M. (2011), “A novel method for nonlinear two-point boundary value problems: combination of ADM and RKM”, Applied Mathematics and Computation, 2011, Vol. 217, No. 9, pp. 4676--4681.
  38. Hassani, A., Hojjati, M.H., Farrahi, G. and Alashti, R.A. (2011), “Semi-exact elastic solutions for thermo- mechanical analysis of functionally graded rotating disks”, Composite Structures, 2011, Vol. 93, No. 12, pp. 3239-51.
  39. Hasseine, A., Bellagoun, A. and Bart, H.-J., “Analytical solution of the droplet breakup equation by the Adomian decomposition method”, Applied Mathematics and Computation, 2011, Vol. 218, No. 5, pp. 2249--2258.
  40. Hetmaniok, E., Słota, D., Wituła, R., and Zielonka, A., “Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem”, Computers and Mathematics with Applications, 2011, Vol. 61, No. 8, pp. 1931--1934.
  41. Hryniewicz, Z. (2011), “Dynamics of Rayleigh beam on nonlinear foundation due to moving load using Adomian decomposition and coiflet expansion”, Soil Dynamics and Earthquak e Engineering, Vol. 31 No. 8, pp. 1123-31.
  42. Hussin, C.H.C., and Kiliçman, A., On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method, Mathematical Problems in Engineering, 2011, Volume 2011, Article ID 724927, 19 pages http://dx.doi.org/10.1155/2011/724927
  43. Jafari, H., Khalique, C.M., and Nazari, M., “Application of the Laplace decomposition method for solving linear and nonlinear fractional diffusion-wave equations”, Applied Mathematics Letters, 2011, Vol. 24, No. 11, pp. 1799--1805.
  44. Khan, Y. and Faraz, N., “Application of modified Laplace decomposition method for solving boundary layer equation”, Journal of King Saud University – Science, 2011, Vol. 23, No. 1, pp. 115--119.
  45. Khan, Y. and Faraz, N. (2011b), “Modified fractional decomposition method having integral w.r.t. (dξ)α ”, Journal of King Saud University – Science, 2011, Vol. 23, No. 2, pp. 157--161.
  46. Khan, M., Gondal, M.A., Soleymani, F., A Novel Two Step Laplace Decomposition Algorithm for Fredholm Integro-Differential Equations, World Applied Sciences Journal, 2011, Vol. 13, (10): 2258-2262.
  47. Khan, M. and Hussain, M., Application of Laplace decomposition method on semi-infinite domain, Numer Algor (2011) 56:211–218 doi: 10.1007/s11075-010-9382-0
  48. Khan, Y., Wu, Q., Faraz, N., Yildirim, A., Three-Dimensional Flow Arising in the Long Porous Slider: An Analytic Solution,  Zeitschrift fur Naturforschung A, 2011, Vol. 66, Issue 8-9, pp. 507-551; https://doi.org/10.5560/zna.2011-0008
  49. Kim, W. and Chun, C., A Modified Adomian Decomposition Method for Solving Higher-OrderSingular Boundary Value Problems, Mathematical Theory and Modeling, 2011 (Online), Vol.2, No.1, 2011
  50. Kipper, C.J., Goulart, A., Degrazia, G., Vilhena, M.T. and Soares, P.M. (2011), “Theoretical study of the decaying convective turbulence in a shear-buoyancy PBL”, Physica A: Statistical Mechanics and its Applications, Vol. 390, No. 20, pp. 3320--3328.
  51. Koochi, A. and Abadyan, M. (2011), “Evaluating the ability of modified Adomian decomposition method to simulate the instability of freestanding carbon nanotube: comparison with conventional decomposition method”, Journal of Applied Sciences, 2011, Vol. 11, No. 11, pp. 3421-8, doi:10.3923/jas.2011.3421.3428
  52. Koochi, A., Kazemi, A.S., Noghrehabadi, A., Yekrangi, A. and Abadyan, M. (2011), “New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets”, Materials and Design, 2011, Vol. 32, No. 5, pp. 2949--2955.
  53. Kundu, B. and Bhanja, D. (2011), “An analytical prediction for performance and optimum design analysis of porous fins”, International Journal of Refrigeration, 2011, Vol. 34, No. 1, pp. 337--352.
  54. Kundu, B. and Wongwises, S. (2011), “A decomposition analysis on convecting-radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient”, Journal of the Frank lin Institute, doi:10.1016/j.jfranklin.2011.12.002
  55. Ekaterina Kutafina. Taylor Series for Adomian Decomposition Method, International Journal of Computer Mathematics, Volume 88, 2011, Issue 17, Pages 3677--3684.
  56. Li, H., Cheng, B., and Kang, W., Application of Adomian decomposition method in laminar boundary layer problems of a kind, 2011 International Conference on Control, Automation and Systems Engineering (CASE), July 30-31, 2011, IEEE, doi:10.1109/ICCASE.2011.5997687.
  57. Mao, Q. (2011), “Free vibration analysis of multiple-stepped beams by using Adomian decomposition method”, Mathematical and Computer Modelling, 2011, Vol. 54 Nos 1/2, pp. 756--764.
  58. Ongun, M.Y. (2011), The Laplace Adomian decomposition method for solving a model for HIV infection of CD4+T cells, Mathematical and Computer Modelling, 2011, Volume 53, Issues 5–6, March 2011, Pages 597-603; https://doi.org/10.1016/j.mcm.2010.09.009 cells
  59. Patel, A. and Serrano, S.E. (2011), “Decomposition solution of multidimensional groundwater equations”, Journal of Hydrology, Vol. 397 Nos 3/4, pp. 202--209.
  60. Petersen, C.Z., Dulla, S., Vilhena, M.T.M.B. and Ravetto, P. (2011), An analytical solution of the point kinetics equations with time-variable reactivity by the decomposition method, Progress in Nuclear Energy, Vol. 53 No. 8, pp. 1091--1094.
  61. Qin, X.-Y. and Sun, Y.-P. (2011), “Approximate analytical solutions for a mathematical model of a tubular packed-bed catalytic reactor using an Adomian decomposition method”, Applied Mathematics and Computation, 2011, Vol. 218 No. 5, pp. 1990-6.
  62. Rach, R. and Duan, J.-S. (2011), “Near-field and far-field approximations by the Adomian and asymptotic decomposition methods”, Applied Mathematics and Computation, 2011, Vol. 217 No. 12, pp. 5910--5922.
  63. Rebelo, P. (2011), “An approximate solution to an initial boundary value problem to the one-dimensional Kuramoto-Sivashinsky equation”, International Journal for Numerical Methods in Biomedical Engineering (formerly Communications in Numerical Methods in Engineering), Vol. 27 No. 6, pp. 874--881.
  64. Safari, M. (2011), Application of He’s variational iteration method and Adomian decomposition method to solution for the fifth order Caudrey-Dodd-Gibbon (CDG) equation, 2011, SR (Scientific Research) Applied Mathematics, Vol. 2, pp. 953-8, doi:10.4236/am.2011.28131.
  65. Safari, M., and Danesh, M., Application of Adomian’s Decomposition Method for the Analytical Solution of Space Fractional Diffusion Equation, Advances in Pure Mathematics, 2011, 1, 345-350; doi:10.4236/apm.2011.16062
  66. Sivakumara T.R. and Baiju, S., Shooting Type Laplace–Adomian Decomposition Algorithm for nonlinear differential equations with boundary conditions at infinity, Applied Mathematics Letters, Volume 24, Issue 10, October 2011, Pages 1702--1708. doi: https://doi.org/10.1016/j.aml.2011.04.024 URL: https://core.ac.uk/download/pdf/82018718.pdf
  67. Tripathi, D. (2011), “Peristaltic transport of a viscoelastic fluid in a channel”, Acta Astronautica, 2011, Vol. 68 Nos 7/8, pp. 1379--1385.
  68. Tsai, P.-Y. and Chen, C.-K., Free vibration of the nonlinear pendulum using hybrid Laplace Adomian decomposition method, Communications in Numerical Methods in Engineering, 2011 https://doi.org/10.1002/cnm.1304
  69. Vahdani, H., Chukova, S. and Mahlooji, H. (2011), “On optimal replacement-repair policy for multi-state deteriorating products under renewing free replacement warranty”, Computers and Mathematics with Applications, Vol. 61 No. 4, pp. 840-50.
  70. Vahdani, H., Mahlooji, H. and Jahromi, A.E. (2011), “Warranty servicing for discretely degrading items with non- zero repair time under renewing warranty”, Computers and Industrial Engineering, doi:10.1016/j.cie.2011.08.012.
  71. Wang, L. and Guo, S. (2011), Adomian method for second-order fuzzy differential equation, International Journal of Mathematical and Computer Sciences, 2011, Vol. 7 No. 3, pp. 104-7.
  72. Wang, Z., Zou, L. and Zong, Z. (2011), Adomian decomposition and Padé approximate for solving differential- difference equation, Applied Mathematics and Computation, 2011, Vol. 218 No. 4, pp. 1371-8.
  73. Wazwaz, A.-M. (2011a), “The regularization method for Fredholm integral equations of the first kind”, Computers and Mathematics with Applications, Vol. 61 No. 10, pp. 2981-6.
  74. Wazwaz, A.-M. and Rach, R. (2011), “Comparison of the Adomian decomposition method and the variational iteration method for solving the Lane-Emden equations of the first and second kinds”, Kybernetes, Vol. 40 Nos 9/10, pp. 1305--1318.
  75. Wu, G.-C. (2011), Adomian decomposition method for non-smooth initial value problems, Mathematical and Computer Modelling, 2011, Vol. 54, Nos 9/10, pp. 2104--2108. https://doi.org/10.1016/j.mcm.2011.05.018
  76. Wu, G.-C., Shi, Y.-G. and Wu, K.-T. (2011), “Adomian decomposition method and non-analytical solutions of fractional differential equations”, Romanian Journal of Physics, Vol. 56 Nos 7/8, pp. 873--880.
  77. Younker, J.M. (2011a), “Numerical integration of the chemical rate equations via a discretized Adomian decomposition”, Industrial and Engineering Chemistry Research, 2011, Vol. 50 No. 6, pp. 3100--3109.
  78. Younker, J.M. (2011b), Supporting information for: numerical integration of the chemical rate equations via a discretized Adomian decomposition.

Reference List for ADM, 2012

  1. Aly, E.H., Ebaid, A., and Rach, R., Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions, Computers and Mathematics with Applications, 2012, Vol. 63, No. 6, pp. 1056--1065.
  2. Almazmumy, M., Hendi, F.A., Bakodah, H.O., Almuzi, H., Recent modifications of adomian decomposition method for initial value problem in ordinary differential equations, American Journal of Computational Mathematics, 2012, Vol. 2, 228-234 http://dx.doi.org/ 10.4236/ajcm.2012.23030
  3. Bakodah, H.O., Some Modifications of Adomian Decomposition Method Applied to Nonlinear System of Fredholm Integral Equations of the Second Kind, International Journal of Contemporary Mathematical Sciences, 2012, Vol. 7, 2012, no. 19, 929 - 942
  4. Behzadi, S.S., Numerical Solution of Sawada-Kotera equation byusing Iterative Methods, Int. J. Industrial Mathematics2012, Vol.4, No. 3, Article ID IJIM-00283, 20 pages; http://ijim.srbiau.ac.ir
  5. Bhanja, D. and Kundu, B., “Radiation effect on optimum design analysis of a constructal T-shaped fin with variable thermal conductivity”, Heat and Mass Transfer, 2011, Vol. 48, No. 1, pp. 109--122.
  6. Blanco-Cocom, L., Estrella, A.G., Avila-Vales, A., Solving delay differential systems with history functions by the Adomian decomposition method, Applied Mathematics and Computation, 2012, Volume 218, Issue 10, 15 January 2012, Pages 5994-6011; https://doi.org/10.1016/j.amc.2011.11.082
  7. Bougoffa, L., Al-Haqbani, M. and Rach, R., “A convenient technique for solving integral equations of the first kind by Adomian decomposition”, Kybernetes, 2012, Vol 41, Issue 1/2, pp. 145--156, doi: 10.1108/03684921211213179
  8. Dhaigude, D.B., Birajdar, G.A., Nikam, V.R., Adomian decomposition method for fractional Benjamin-Bona-Mahony-Burger equations, International Journal of Applied Mathematics and Mechanics, 2012, Vol. 8, pp. 42--51.
  9. Doğan, N., Solution of the system of ordinary differential equations by combined Laplace transform--Adomian decomposition method, Mathematical and Computational Applications, 2012, Vol. 17, No. 3, pp. 203-211,
  10. Duan, J.-S. Chaolu, T., and Rach, R., Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method, Applied Mathematics and Computation, 2012, Volume 218, Issue 17, 1 May 2012, Pages 8370-8392; https://doi.org/10.1016/j.amc.2012.01.063
  11. Duan, J.-S. and Rach, R. (2012a), Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms, Computers and Mathematics with Applications, 2012, Vol. 63, Issue 11, pp. 1557--1568. https://doi.org/10.1016/j.camwa.2012.03.050
  12. Duan, J.-S., Rach, R., Băleanu, D., and Wazwaz, A.-M., A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in Fractional Calculus, 2012, Vol. 3, No. 2, pp. 73--99.
  13. Duan, J.-S., Rach, R., Wang, Z. (2012b), “On the effective region of convergence of the decomposition series solution”,  Journal of Algorithms & Computational Technology, 2012, Vol. 7, No. 2, pp. 227--247; doi: 10.1260/1748-3018.7.2.227
  14. Duan, J.-S., Rach, R., and Wazwaz, A.-M., “Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems”,
  15. Duan, J.-S., Temuer, C.-L. and Rach, R., Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method, Applied Mathematics and Computation, 2012, Vol. 218, No. 17, pp. 8370--8392. doi:10.1016/j.amc.2012.01.063
  16. Elsaid, A., Adomian polynomials: a powerful tool for iterative methods of series solution of nonlinear equations, Journal of Applied Analysis and Computation, 2012, Vol. 2, No 4, pp. 381--394.
  17. Ghehsareh, H.R., Abbasbandy, S., Soltanalizadeh, B., Analytical Solutions of the Slip Magnetohydrodynamic Viscous Flow over a Stretching Sheet by Using the Laplace–Adomian Decomposition Method,  Zeitschrift für Naturforschung A, 2012, Volume 67a, Issue 5, pp. 248--254; doi: 10.5560/ZNA.2012-0010
  18. Hasan, Y.Q., Solving first-order ordinary differential equations by Modified Adomiandecomposition method, Advances in Intelligent Transportation Systems (AITS), 2012, Vol. 1, No. 4, 2012, pp. 86--90.
  19. Hasan, Y.Q., Modified Adomian decomposition method for second ordersingular initial value problems, Advances in Computational Mathematics, 2012, Vol. 1, No. 2, pp. 94--99.
  20. Hasan, Y.Q., The numerical solution of third-order boundary value problems by the modified decomposition method, Advances in Intelligent Transportation Systems (AITS), 2012, Vol. 1, No. 3, 2012, 71--74.
  21. Hendi, F.A., Bakodah, H.O., Almazmumy, M., and Alzumi, H., “A Simple Program for Solving Nonlinear Initial Value Problem Using Adomian Decomposition Method,” International Journal of Reseach and Reviews in Applied Science, 2012, Vol. 12, No. 3,
  22. Ibijola, E.A. and Adegboyegun B.J., A comparison of Adomian’s decomposition method and Picard iterations method in solving nonlinear differential equations, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 2012, Volume 12, Issue 7, Version 1.0; Online ISSN: 2249-4 626 & Print ISSN: 0975-5896
  23. Khan, M., Gondal, M., Kumar, S., A new analytical solution procedure for nonlinear integral equations, Mathematical and Computer Modelling, 2012, Volume 55, Issues 7–8, April 2012, Pages 1892-1897. https://doi.org/10.1016/j.mcm.2011.11.044
  24. Koochi, A. and Abadyan, M. (2012), “Efficiency of modified Adomian decomposition for simulating the instability of nano-electromechanical switches: comparison with the conventional decomposition method”, Trends in Applied Sciences Research, 2012, Vol. 7, No. 1, pp. 57-67, doi:10.3923/tasr.2012.57.67
  25. Koochi, A., Kazemi, A.S., Khandani, F. and Abadyan, M. (2012), “Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations”, Physica Scripta, 2012, Vol. 85, No. 3, 035804, doi:10.1088/0031-8949/85/03/035804
  26. Lin, Y., Liu, Y., and Li, Z.,Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions, Computer Physics Communications, 2012, Volume 183, Issue 1, January 2012, Pages 106-117; https://doi.org/10.1016/j.cpc.2011.08.001
  27. Liu, Y., A modified Adomian decomposition method, World Academy of Science, Engineering and Technology, 2012, Vol.65. International Conference on Computer, Electrical, and Systems Sciences.
  28. Mahmoudi, Y., Abdollahi M, Karimian N, Khalili H., ADM with Laguerre polynomials for solving ordinary differential equations. Journal of Basic and Applied Scientific Research, 2012, Vol. 2, No. 12, pp. 12236--12241.
  29. Manafianheris, J., Solving the integro-differential equations using the modified Laplace Adomian decomposition method, Journal of Mathematical Extension, 2012, Vol. 6, No. 1, pp. 65--79.
  30. Mao, Q., Free Vibration Analysis of Uniform Beams with Arbitrary Number of Cracks by using Adomian Decomposition Method, World Applied Sciences Journal, 2012, Vol. 19 (12): 1721-1730; doi: 0.5829/idosi.wasj.2012.19.12.2581
  31. Mobasher, A.A., Biazar, A.P., Deng, Z., Piecewise Nth order Adomian Polynomial stiff differential equation solver, International Journal of Modern Engineering, 2012, Vol. 13, No. 1, 2012, pp. 13-17.
  32. Mohammadhosseini, B., Niknam, A.R., Majedi, S. and Shokri, B. (2012), “Study of nonlinear dynamics of the filamentation instability in a current-carrying plasma using Adomian decomposition method”, IEEE Transactions on Plasma Science, 2012, Vol. 40 No. 1, pp. 9-15.
  33. Pue-on, P. and Viriyapong, N., Modified Adomian Decomposition Method for Solving Particular Third-Order Ordinary Differential Equations, Applied Mathematical Sciences, 2012, Vol. 6, 2012, no. 30, 1463 - 1469.
  34. Rach, R., “A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011”, Kybernetes, 2012, vol. 41, pp. 1087–1148.
  35. Raslan, K.R., Soliman, A.A., Ali, A.H., A comparison between the variational iteration method and Adomian decomposition method for the FitzHugh-Nagumo equations, International Journal of Physical Sciences, 2012, Vol. 7(15), pp. 2302 - 2309, doi: 10.5897/IJPS12.174
  36. Salekdeh, A.Y., Koochi, A., Beni, Y.T. and Abadyan, M. (2012), “Modeling effects of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: material size dependency, van der Waals force and non-classic support conditions”, Trends in Applied Sciences Research, Vol. 7 No. 1, pp. 1-17, doi:10.3923/tasr.2012.1.17.
  37. Sheikholeslami, M., Ganji, D.D., Ashorynejad, H.R. and Rokni, H.B. (2012), “Analytical investigation of Jeffery- Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method”, Applied Mathematics and Mechanics (English Edition), 2012, Vol. 33 No. 1, pp. 25-36.
  38. Soliman, A.A., Numerical Simulation of the FitzHugh-Nagumo Equations, Hindawi Publishing Corporation Abstract and Applied Analysis, Volume 2012, Article ID 762516, 13 pages doi:10.1155/2012/762516
  39. Soroush, R., Koochi, A., Kazemi, A.S. and Abadyan, M. (2012), “Modeling the effect of van der Waals attraction on the instability of electrostatic cantilever and doubly-supported nano-beams using modified Adomian method”, International Journal of Structural Stability and Dynamics, 2012, Vol. 12, No. 5, https://doi.org/10.1142/S0219455412500368
  40. Vahidi, A.R., Azimzadehaand, Z., and Mohammadifar, S., Restarted Adomian Decomposition Methodfor Solving Duffing-van der Pol Equation, Applied Mathematical Sciences, 2012, Vol. 6, No. 11, 499--507.
  41. Vahidi, A.R. and Hasanzade, M. (2012), Restarted Adomian’s decomposition method for the Bratu-type problem, Applied Mathematical Sciences, Vol. 6 No. 10, pp. 479--486.
  42. Zhang, Y., Chong, K.T., Kazantzis, N. and Parlos, A.G. (2012), Discretization of nonlinear input-driven dynamical systems using the Adomian decomposition method, Applied Mathematical Modelling, 2012, Vol. 36, Issue 12, pp. 5856--5875. https://doi.org/10.1016/j.apm.2012.01.030

Reference List for ADM, 2013

  1. Al-Hayani, W., Solving nth-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method, Applied Mathematics, 2013, Vol 4, No 6, 5 pages, doi: 10.4236/am.2013.46121
  2. Bildik, N., and Inc, M., A comparison between Adomian decomposition and Tau methods, Hindawi Publishing Corporation, Abstract and Applied Analysis, Volume 2013, Aticle ID 621019 5 pages, doi: 10.1155/2013/621019
  3. Bolujo, A., Sunday, F., A Semi-Analytic method for Solving Nonlinear Partial Differential Equations, Mathematical Theory and Modeling, 2013, Vol.3, No.5, 5 pages.
  4. Bougoffa, L., Rach, R.C., El-Manouni, S., A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations, International Journal of Computer Mathematics, 2013, Volume 90, Issue 2, pages 360--375; https://doi.org/10.1080/00207160.2012.718073
  5. Cano, J.A.S., Adomian decomposition method and Taylor series method in ordinary differential equations, JRRAS, 2013, Vol. 16, No. 2, pp. 168--175.
  6. Duan, J.-S., Chaolu, T., Rach, R., Lu, L., The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations, Computers & Mathematics with Applications, 2013, Volume 66 Issue 5, pp. 728--736; doi: 10.1016/j.camwa.2013.01.019
  7. Duan, J.-S., Rach, R., and Lin, S.M., Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique Mathematical Methods in Applied Sciences, 2013, Volume 36, Number 13, pp. 1790-1804; https://doi.org/10.1002/mma.2725
  8. Duan, J.-S., Rach, R., and Wang, Z., On the effective region of convergence of the decomposition series solution, Journal of Algorithms and Computational Technology, Volume 7, 2013, 227--247.
  9. Duan, J.-S., Rach, R., and Wazwaz, A.-M., A new modified Adomian decomposition method for higher-order nonlinear dynamical systems, CMES: Computer Modeling in Engineering & Sciences, 2013, Vol. 94, No. 1, 2013, pp. 77--118.
  10. Duan, J.-S., Rach, R., Wazwaz, A.-M., Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems, International Journal of Non-Linear Mechanics, 2013, Volume 49, 2013, Pages 159--169; doi: 10.1016/j.ijnonlinmec.2012.10.003 159--169.
  11. Duan, J.-S., Rach, R., Wazwaz, A.-M., Chaolu, T.; Wang, Z., A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions, Applied Mathematical Modelling, 2013, vol. 37, pp. 8687–8708.
  12. Duan, J.-S., Wang, Z., Fu, S.-Z., Chaolu, T., Parametrized temperature distribution and efficiency of convective straight fins with temperature-dependent thermal conductivity by a new modified decomposition method, International Journal of Heat and Mass Transfer, 2013, Volume 59, April, Pages 137--143; https://doi.org/10.1016/j.ijheatmasstransfer.2012.11.080
  13. Ebaid, A., Al-Armani, N., A new approach for a class of the Blasius problem via a yransformation and Adomian’s method, Abstract and Applied Analysis, Volume 2013, Article ID 753049, 8 pages http://dx.doi.org/10.1155/2013/753049
  14. Fu, S.-Z., Wang, Z., Duan, J.-S., Solution of quadratic integral equations by the Adomiandecomposition method, CMES: Computer Modeling in Engineering & Sciences, 2013, vol.92, no.4, pp.369-385, 2013
  15. Kolebaje, O.T., Ojo, O.L., Akinyemi, P., and Adenodi, R.A., On the application of the multistage laplace adomian decomposition method with pade approximation to the rabinovich-fabrikant system, Advances in Applied Science Research, 2013, 4(3):232-243
  16. Koochi, A., Abadyan, M., Hosseini-Toudeshky, H,. and Ovesy, H.R., Modeling the influence of surface effect on the instability of beam type NEMS in the presence of van der Waals force, International Journal of Structural Stability and Dynamics, 2013, Vol. 13, No. 04, 1250072 https://doi.org/10.1142/S0219455412500721
  17. Lin, Y., Liu, Y., Li, Z., Symbolic computation of analytic approximate solutions for nonlinear differential equations with boundary conditions, Applied Mathematics and Computation, Volume 222 (2013) 145–166. https://doi.org/10.1016/j.amc.2013.06.076
  18. Lin, Y., Liu, Y., Li, Z., Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations, Computer Physics Communications, Volume 184 (2013) 130–141. https://doi.org/10.1016/j.cpc.2012.07.015
  19. Rach, R., Wazwaz, A.-M., and Duan, >J.-S., A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations, Kybernetes, 2013, Vol. 42, No 2, pp. 282--308, doi: 10.1108/03684921311310611
  20. Rehman, M.S., Yaseen, M., Kamran, T., New Iterative Method for Solution of System of linear Differential Equations, International Journal of Science and Research (IJSR), 2013, 6(14)
  21. Saravanan, A. and Magesh, N., A comparison between the reduced differentialtransform method and the Adomian decompositionmethod for the Newell–Whitehead–Segel equation, Journal of the Egyptian Mathematical Society, 2013, Vol. 21, Issue 3, pp. 259--265. https://doi.org/10.1016/j.joems.2013.03.004
  22. Wazwaz, A.-M., Rach, R., and Duan, J.-S., Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions, Applied Mathematics and Computation, 2013, vol. 219, no. 10, pp. 5004–5019, 2013. https://doi.org/10.1016/j.amc.2012.11.012
  23. Xie, L.-J., A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind, Journal of Applied Mathematics, 2013, Volume 2013, Article ID 795015, 7 pages http://dx.doi.org/10.1155/2013/795015

Reference List for ADM, 2014

  1. Adam, B.A.A., A comparative study of Adomian decomposition method and He--Laplace method, Applied Mathematics, 2014, Vol. 5, No. 21, doi: 10.4236/am.2014.521312
  2. Waleed Al-Hayani, "Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems," Applied Mathematics, 2014, Vol.05, No.10, 10 pages, doi: 10.4236/am.2014.510136
  3. Al-Sawoor, A.J., and Al-Amr, M.O., A new modification of variational iteration methodfor solving reaction–diffusion system with fastreversible reaction, Journal of the Egyptian Mathematical Society, 2014, Vol. 22, pp. 396--401.
  4. Aski, F.S., Nasirkhani, S.J., Mohammadian, E., and Asgari, A., Application of Adomian decomposition method for micropolar flow in a porous channel, Propulsion and Power Research, 2014, Vol. 3, Issue 1, pp. 15--21.
  5. Badradeen A. A. Adam, A Comparative Study of Adomain Decompostion Method and He-Laplace Method, Applied Mathematics, 2014, Vol.05 No.21, Article ID:51995,11 pages 10.4236/am.2014.521312
  6. Bougoffa, L., The Adomian Decomposition Method for Solving a Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue, ScientificWorldJournal. 2014; 2014: 579628. doi: 10.1155/2014/579628
  7. Jun-Sheng Duan, "Higher-Order Numeric Solutions for Nonlinear Systems Based on the Modified Decomposition Method," Journal of Applied Mathematics and Physics, 2014, Vol 2, No. 1, 1--7. doi: 10.4236/jamp.2014.21001
  8. Duan, J.-S., Rach, R., Wazwaz, A.-M., A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method, Open Engineering, 2014, Volume 5, Issue 1, 59-74, 2014, doi: 10.1515/eng-2015-0007
  9. Ebaid, A., Al Mutairi, F., and Khaled, S.M., Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO 2 -Water Nanofluids in the Presence of a Magnetic Field, Advances in Mathematical Physics, Volume 2014, Article ID 538950, 9 pages http://dx.doi.org/10.1155/2014/538950
  10. El-Sayed, A.M.A., Hashem, H.H.G., and Ziada, E.A.A., Picard and Adomian decomposition methods for a quadratic integral equation of fractional order, Journal of Computational and Applied Mathematics, 2014, 33, Issue 1, pp. 95--109, doi: 10.1007/s40314-013-0045-3
  11. Fatoorehchi, H., Abolghasemi, H., Rach, R., An accurate explicit form of the Hankinson--Thomas--Phillips correlation for prediction of the natural gas compressibility factor, Journal of Petroleum Science and Engineering, 2014, Volume 117, pp. 46--53. doi: 10.1016/j.petrol.2014.03.004
  12. Fatoorehchi, H., Abolghasemi, H., Rach, R., Assar, M., An improved algorithm for calculation of the natural gas compressibility factor via the Hall-Yarborough equation of state, The Canadian Journal of Chemical Engineering, 2014, Volume 92, Issue 12, 2014, pp. 2211--2217. https://doi.org/10.1002/cjce.22054
  13. Ghazanfari, B. and Sepahvandzadeh, A., Adomian Decomposition Method for Solving Fractional Bratu-type Equations, Journal of Mathematics and Computer Science, 2014, Vol. 8, Issue 3, pp. 236--244; http://dx.doi.org/10.22436/jmcs.08.03.06
  14. Hasan, Y.Q., A new development to the Adomian decomposition for solving singular IVPs of Lane--Emden Type, United States of America Research Journal (USARJ), 2014, Vol. 2, No.3, 2014, ISSN 2332-2160
  15. Lin, Y. and Chen, C.K., Modified Adomian decomposition method for double singular boundary value problems, 2014, on line
  16. Maitama, S., A New Approach to Linear and NonlinearSchrödinger Equations Usingthe Natural Decomposition Method, International Mathematical Forum, 2014, Vol. 9, 2014, no. 17, 835 - 847.
  17. Mobasher, A., BUdak, S., Laplace--Adomian solutions for classical fluid dynamics problems, International Journal of Modern Engineering, 2014, Volume 14, No. 2, pp. 62--68.
  18. Narayanamoorthy, S. and Yookesh, T.L. An Adomian decomposition method to solve linear fuzzy differential equations, Proceeding of the International Conference on Mathematical Methods and Computation, Jamal Mohamed College (Autonomous), Tiruchirapalli, India, 13-14 February 2014.
  19. Qin, X.-Y., Duan, Y.-X., and Yin, M.-R., Approximate analytic solutions for the two-phase Stefan problem using the Adomian decomposition method, Journal of Applied Mathematics, Volume 2014, Article ID 391606, 6 pages; http:/dx.doi.org/10.1155/2014/391606
  20. Rach, R., Wazwaz, A.-M., Duan, J.-S., Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method, Journal of Mathematical Chemistry, 2014, Volume 52, Issue 1, pp 255–267.
  21. Rach, R., Wazwaz, A.-M., Duan, J.-S., A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, International Journal of Biomathematics, Vol. 07, No. 02, March 2014, 1450020 (2014) [12 pages].
  22. Ray, S.S., New Approach for General Convergence of the Adomian Decomposition Method, World Applied Sciences Journal, 2014, Vol. 32, No. 11, pp. 2264--2268; doi: 10.5829/idosi.wasj.2014.32.11.1317
  23. Sari, M.R., Kezzar, M., Adjabi, R., A comparison of Adomian and generalized Adomian methods in solving the nonlinear problem of flow in convergent-divergent channels, Applied Mathematical Sciences, 2014, Vol. 8, no. 7, 321 - 336; http://dx.doi.org/10.12988/ams.2014.39495
  24. Wazwaz, A.-M., Rach, R., Duan, J.-S., A study on the systems of the Volterra integral forms of the Lane-Emden equations by the Adomian decomposition method, Mathematical methods in the Applied Siences, 2014, Vol. 37, issue 1, pp. 10-19; https://doi.org/10.1002/mma.2776
  25. Yassien, S.M., Modification Adomian Decomposition Method for solving Seventh Order Integro-Differential Equations, IOSR Journal of Mathematics, 2014, Volume 10, Issue 5.

Reference List for ADM, 2015

  1. Akoan, I.P., Adomian Decomposition Approach to the Solution of the Burger’s Equation, American Journal of Computational Mathematics, 2015, 5, 329-335
  2. Az-Zo'bi, E.A., New Applications of Adomian Decomposition Method, Middle-East Journal of Scientific Research 2015, Vol. 23 (4): 735-740; doi: 10.5829/idosi.mejsr.2015.23.04.22004
  3. Bengochea, G. and Verde‐Star, L., An operational approach to the Emden–Fowler equation, Mathematical Methods in the Applied Sciences, 2015, https://doi.org/10.1002/mma.3415
  4. Benhammouda, B., Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method, SpringerPlus, 2015, Article number: 648. doi: 10.1186/s40064-016-2208-3
  5. Bildik, N., Deniz, S., Modified Adomian decomposition method for solving Riccati differential equations, Review of the Air Force Academy, 2015, vol. 3, no. 30, pp. 21–26; doi: 10.19062/1842-9238.2015.13.3.3
  6. Cakir, M., Arslan, D., The Adomian Decomposition Method and the Differential Transform Method for Numerical Solution of Multi-Pantograph Delay Differential Equations, Applied Mathematics, 2015, AM> Vol.6 No.8, pp. 1332--1343. doi: 10.4236/am.2015.68126
  7. Chowdhury, M.S.H., Hashim, I., Hosen, M.A., Solving Linear and Non-Linear Stiff System of Ordinary Differential Equations by Multistage Adomian Decomposition Method, Proc. of TheThirdIntl. Conf. On Advances in Applied Science and Environmental Technology, -ASET 2015
  8. Duan, J.-S. and Rach, R., The degenerate form of the Adomian polynomials in the power series method for nonlinear ordinary differential equations, Journal of Mathematics and System Science, 2015, Volume 5, Pages 411--428, doi: 10.17265/2159-5291/2015.10.003
  9. Duan, J.-S., Rach, R., Wazwaz, A.-M., Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method, Journal of Mathematical Chemistry, 2015, Volume 53, Issue 4, pp 1054–1067.
  10. Fatoorehchi, H., Abolghasemi, H., and Rach, R., A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis-Menten type nonlinearities, Fluid Phase Equilibria, 2015, Vol. 395, pp. 44--50. https://doi.org/10.1016/j.fluid.2015.03.024
  11. Fatoorehchi, H., Rach, R., Abolghasemi, H., A novel family of iterative schemes for computation of matrix inverses by the Adomian decomposition method, Romanian Journal of Physics, 2015, Vol. 60, No. 9, pp. 1315--1327.
  12. Fatoorehchi, H., Rach, R., Tavakoli, O., and Abolghasemi, H., An efficient numerical scheme to solve a quintic equation of state for supercritical fluids, Chemical Engineering Communications, Vol. 202, No. 3, 2015, Pp. 402--407. https://doi.org/10.1080/00986445.2013.843529
  13. Gurrala, G., Dimitrovski, A,D., Pannala, S., Simunovic, S,, Starke, M.R., and Sun, K., Application of Adomian Decomposition for Multi-Machine Power System Simulation. United States: N. p., 2015. Conference: 2015 IEEE PES General Meeting, Denver, CO, USA, 20150726, 20150730. https://www.osti.gov/biblio/1265735
  14. Kaliyappan, M. and Hariharan, S., Symbolic Computation of Adomian Polynomials Based on Rach’s Rule, British Journal of Mathematics & Computer Science, 2015, Volume 5, Issue 5, pp. 562--570, Article no.BJMCS.2015.041
  15. Kumar, A, and Pankaj, R.D., Laplace -Modified Decomposition Method for the Generalized Hirota-Satsuma Coupled KdV Equation, Canadian Journal of Basic and Applied Sciences, 2015, Vol. 03, No. 4.
  16. Molabahrami, A., A practical review of the Adomian decomposition method: computer implementation aspects, Iranian Journal of Numerical Analysis and Optimization, 2015, Vol. 5, No. 2, pp 29-43
    17. mola
  17. Nigam, R., A new formulation of Adomian polynomials, International Journal of Mathematics and Scientific Computing, 2015, Vol. 5, No. 2, pp. 92--97.
  18. Rach, R., Wazwaz, A.-M., Duan, J.-S., The Volterra integral form of the Lane-Emden equation: New derivations and solution by the Adomian decomposition method, Journal of Applied Mathematics and Computing, 2015, Volume 47, Issue 1–2, pp 365–379 |
  19. Rach, R., Duan, J.-S., Wazwaz, A.-M., On the solution of non-isothermal reaction-diffusion model equations in a spherical catalyst by the modified Adomian method, Chemical Engineering Communications, 2015, Volume 202, 2015 - Issue 8, pp. 1081--1088; https://doi.org/10.1080/00986445.2014.900054
  20. Sekar, S. and Nalini, M., Numerical Solution of the Linear and Nonlinear Stiff ProblemsUsing Adomian Decomposition Method, 2015, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 5 Ver. IV(Sep. -Oct. 2015), pp. 14-20.
  21. Shehata, M.S.M., A Study of Some Nonlinear Partial Differential Equations by Using Adomian Decomposition Method and Variational Iteration Method, American Journal of Computational Mathematics, 2015, Vol.5 No.2, pp. 195--203. doi: 10.4236/ajcm.2015.52016
  22. Tabet, I., Kezzar, M., Touafek, K., Bellel, N., Gherieb, S., Khelifa, A., and Adouane, M., Adomian Decomposition Method and Pade Approximation to Determine fin Efficiency of Convective Straight Fins in Solar Air Collector, International Journal of Mathematical Modelling & Computations, 2015, Vol. 05, No. 04, 335--346.
  23. Taiwo, O.A. and Hassan, M.O., Approximation of Higher-order Singular Initial and Boundary Value Problems by Iterative Decomposition and Bernstein Polynomial Methods, British Journal of Mathematics & Computer Science, 2015, Vol. 9, No. 6, pp. 498--515, 2015, Article no.BJMCS.2015.221
  24. Wattanasakulpong, N. and Chaikittiratana, A., Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions, Mechanics Based Design of Structures and Machines, 2015, Vol. 44, No. 3, 2015, Pp. 270-282. http://dx.doi.org/10.1080/15397734.2015.1055762

Reference List for ADM, 2016

  1. Adair, D. and Jaeger, M., Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method, Applied Mathematical Modelling, 2016, Vol. 40, Issue 4, pp. 3230-3241, https://doi.org/10.1016/j.apm.2015.09.097
  2. Alkresheh, H.A., New classes of Adomian polynomials for the Adomian decomposition method, International Journal of Engineering Science Invention, 2016, Volume 5, Issue 3, pp. 37--44.
  3. Alkresheh, H.A. and Ismail, A.I.M., An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method, Journal of Interpolation and Approximation in Scientific Computing, 2016, Volume 2016, No. 1, Pages 25-37 Article ID jiasc-00090, 13 Pages doi: 10.5899/2016/jiasc-00090
  4. Benhammouda, B., A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method, Springerplus, 2016, May 11; 5:590. doi: 10.1186/s40064-016-2208-3
  5. Brahim, B., Solution of constrained mechanical multibody systems using Adomian decomposition method, 2016;
  6. Dimitrovski, A.D., Simunovic, S., Pannala, S., Numeric Modified Adomian Decomposition Method for Power System Simulations, Conference: IEEE Power & Energy Society (PES) sponsored International Conference on Power Systems Technology (POWERCON), Wollongong, Australia, 20160928, 20161001.
  7. Fatheah Ahmed Hendi and Manal Mohamed Al-Qarni, "Comparison between Adomian’s Decomposition Method and Toeplitz Matrix Method for Solving Linear Mixed Integral Equation with Hilbert Kernel," American Journal of Computational Mathematics, 2016, Vol.06, No.02, 7 pages, doi: 10.4236/ajcm.2016.62019
  8. González-Gaxiola, O., Bernal-Jaquez, R., Applying Adomian decomposition method to solve Burgess equation with a non-linear source, 2016.
  9. González-Gaxiola, O., de Chávez, J.R., Santiago, J.A., A Nonlinear Option Pricing Model Through the Adomian Decomposition Method, International Journal of Applied and Computational Mathematics, 2016, Vol. 2, Issue 2, pp. 453--467; https://doi.org/10.1007/s40819-015-0070-6
  10. Gurrala, G., Batageri, A., Dinesha, D.L., Real-time simulation of power converters using Adomian decomposition method on mini-FSS, Published in IEEE International Conference on Power…, online: http://toc.proceedings.com/34316webtoc.pdf 2016, doi: 10.1109/PEDES.2016.7914521
  11. Kataria, K.K. and Vellaisamy, Simple parametrization methods for generating Adomian polynomials, Applicable Analysis and Discrete mathematics, 2016, Vol. 10, N. 01, pp. 168--185; doi: 10.2298/AADM160123001K available online at http://pefmath.etf.rs
  12. Mageswari M. and Nirmala M., Stagnation point flow over a stretching sheet with Newtonian heating using Laplace Adomian decomposition method, International Journal of Pure and Applied Mathematics, Volume 110, No. 1, 2016, 95--102 url: http://www.ijpam.eu doi: 10.12732/ijpam.v110i1.11
  13. Mohamed, A.S. and Mahmoud, R.A., Picard,Adomian and predictor–corrector methods for an initial value problem of arbitrary (fractional) orders differential equation, Journal of the Egyptian Mathematical Society, 2016, Vol. 24, pp. 165–170.
  14. Naeem, M., Mushtaq, M., Ahmad, J., Decomposition Method for Kdv Boussinesq andCoupled Kdv Boussinesq Equations, Mathematical Theory and Modeling, 2016, Vol. 6, No.9,
  15. Paul, S., Mondal, S.P., Bhattacharya, P., Numerical solution of Lotka Volterra prey predator model by using Runge–Kutta–Fehlberg method and Laplace Adomian decomposition method, Alexandria Engineering Journal, 2016, Vol. 55, pp. 613--617. doi: 10.1016/j.aej.2015.12.026
  16. Rach, R., Duan, J.-S., Wazwaz, A.-M., Solution of Higher-Order, Multipoint, Nonlinear BoundaryValue Problems with High-Order Robin-Type BoundaryConditions by the Adomian Decomposition Method, Applied Mathematics & Information Sciences, 2016, Vol.10, No. 4, 1231--1242. http://dx.doi.org/10.18576/amis/10040

Reference List for ADM, 2017

  1. Akinola, E.I. and Akinpelu, F.O., The Laplace transform series decomposition method for solving nonlinear Volterra integro-differential equations, FUW Trends in Science & Technology Journal, 2017, Vol. 2, No. 1A, pp. 96--100. www.ftstjournal.com
  2. Al-Mazmumy M. and Almuhalbedi, S.O., “Restarted Adomian Decomposition Method for Solving Volterra’s Population Model”, American Journal of Computational Mathematics, 2017, Vol.07, No.02, doi: 10.4236/ajcm.2017.72016
  3. Alshaery, A. and Ebaid, A., “Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method”, Acta Astronautica, 2017, Volume 140, p. 27--33; doi: 10.1016/j.actaastro.2017.07.034
  4. Dispini, M., Mungkasi, S., Adomian decomposition method used to solve the one-dimensional acoustic equations, Journal of Physics: Conference Series, 2017, Volume 856, Issue 1, article id. 012003. doi: 10.1088/1742-6596/856/1/012003
  5. Duan, J.-S., Rach, R., Wazwaz, A.-M., Higher order numeric solutions of the Lane–Emden-type equations derived from the multi-stage modified Adomian decomposition method, International Journal of Computer Mathematics, 2017, Volume 94, 2017 - Issue 1, pp. 197--215; https://doi.org/10.1080/00207160.2015.1100299
  6. Ebaid, A., Rach, R., El-Zahar, E., A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method, Acta Astronautica, 2017, Volume 138, p. 1-9. doi: 10.1016/j.actaastro.2017.05.006
  7. González-Gaxiola, O., Bernal-Jaquez, R., Applying Adomian Decomposition Method to Solve Burgess Equation with a Non-linear Source, International Journal of Applied and Computational Mathematics, 2017, Volume 3, Issue 1, pp. 213--224. https://doi.org/10.1007/s40819-015-0100-4
  8. González-Gaxiola, O., Santiago, J.A., de Chávez, J.R., Solution for the Nonlinear Relativistic Harmonic Oscillator via Laplace-Adomian Decomposition Method, International Journal of Applied and Computational Mathematics, 2017, Volume 3, Issue 3, pp 2627–2638; https://doi.org/10.1007/s40819-016-0267-3
  9. Hamoud, A.A., Ghadle, K.P., The combined modified Laplace with Adomian decomposition method for solving the noninear Volterra--Fredholm integro-differential equations, Journal KSIAM, 2017, Vol. 21, No. 1, pp. 17--28.
  10. Hamoud, A.A., Ghadle, K.P., The reliable modified of Laplace Adomian decomposition method to solve nonlinear interval Volterra--Fredholm integral equations,  The Korean Journal of Mathematics, 2017, Vol. 25, No 3, pp. 323-334. https://doi.org/10.11568/kjm.2017.25.3.323
  11. Hasanzadeh, M., Osgooel, E., Multistage Adomian Decomposition Method for Solving Initial Value Problem of Bratu-Type, Int. J. Open Problems Compt. Math., Vol. 10, No. 1, March 2017.
  12. Issa, M.S.B., Hamoud, A.A., Ghadle, K.P., Giniswamy, Hybrid method for solving nonlinear Volterra-Fredholm integro-differential equations, Journal Math. Comput. Sci., 2017, Vol. 7, No. 4, pp. 625-641. Available online at http://scik.orgJ.
  13. Patel, T. and Meher, R., Thermal Analysis of porous fin with uniform magnetic field using Adomian decomposition Sumudu transform method, Nonlinear Engineering, 2017, Volume 6, Issue 3, pp.191--200; doi: 10.1515/nleng-2017-0021
  14. Rani, D. and Mishra, V., Approximate solution of boundary value problem with Bernstein polynomial Laplace decomposition method, International Journal of Pure and Applied Mathematics, 2017, Volume 114, No. 4 2017, 823-833
  15. Sekson Sirisubtawee and Supaporn Kaewta, "New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems," International Journal of Mathematics and Mathematical Sciences, 2017, Vol. 2017, Article ID 5742965, 20 pages, https://doi.org/10.1155/2017/5742965
  16. Sunday, J., Convergence analysis and implementation of Adomian decomposition method on second-order oscillatory problems, Asian Research Journal of Mathematics, 2017, Vol. 2, No. 5, pp. 1--12. Article no.ARJOM.32011
  17. Sunday, J., The Duffing oscillator: applications and computational simulations, Asian Research Journal of Mathematics, 2017, Vol. 2, No. 2, pp. 1--13; Article number: ARJOM.31199
  18. Usman, M.A., Hassan, O.R., Ibiyemi, O.M., Steady Flow of a Third Grade Fluid in a Porous Half-Space using Adomian Decomposition Method, Nigerian Journal of Mathematics and Applications, 2017, Vol. 26, pp. 61--82.
  19. Yousif, M.A. and Mahmood, B.A., Approximate solutions for solving the Klein–Gordon and sine-Gordon equations, ournal of the Association of Arab Universities forBasic and Applied Sciences, 2017, Vol. 22, pp. 83--90.
  20. Zaouagui I.N. and Badredine T., New Adomian’s Polynomials Formulas for the Non-linear and Nonautonomous Ordinary Differential Equations, Journal of Applied & Computational Mathematics, 6:373, Vol 6(4) 2017, doi: 10.4172/2168-9679.1000373

Reference List for ADM, 2018

  1. Al-Ashhab, S., Adomian series solution to a Rayleigh power-law problem, Arabian Journal for Science and Engineering, September 2018, Volume 43, Issue 9, pp. 4911--4916. https://doi.org/10.1007/s13369-018-3223-1
  2. Boukary, B., Loufouilou-Mouyedo, J., Bonazebi-Yindoula, J., and Bissanga, G., "Application of the Adomian Decomposition Method (ADM) for Solving the Singular Fourth-Order Parabolic Partial Differential Equation," Journal of Applied Mathematics and Physics, 2018, Vol 06, No 07, 5 pages, doi: 10.4236/jamp.2018.67124
  3. Goyal, K. and Singhal, M., Adomian Decomposition Method for Thermal Analysis of a Furnace, In: Fujita H., Nguyen D., Vu N., Banh T., Puta H. (eds) Advances in Engineering Research and Application. ICERA 2018. Lecture Notes in Networks and Systems, vol 63. Springer, Cham; https://doi.org/10.1007/978-3-030-04792-4_20
  4. Hamoud, A.A., Ghadle, K.P., Existence and Uniqueness of the Solution for Volterra-Fredholm Integro-Differential Equations, Journal of Siberian Federal University. Mathematics & Physics, 2018, 11(6), 692–701.
  5. Keshmiri, A., Wu, N., “A Wideband Piezoelectric Energy Harvester Design by Using Multiple Non-Uniform Bimorphs”, Vibration, 2018, 1(1) 93-104; doi: 10.3390/vibration1010008
  6. Keshmiri, A., Wu, N., Wang, Q., “Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method”, International Journal of Structural Stability and Dynamics”, 2018, Vol. 18, No. 07, 1850101 (2018) https://doi.org/10.1142/S0219455418501018
  7. Lin, Y., Yang, J.-T., Chen, R., Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method, Results in Physics, 2017, Volume 9, p. 1677-1684; doi: 10.1016/j.rinp.2018.01.074
  8. Lisbôa, T.V., Marczak, R.J., (2018) Adomian decomposition method applied to moderately anisotropic thick plates in linear bending, European Journal of Mechanics-A/Solids, 2018, Vol/ 70, :95–114
  9. Lisbôa, T.V., Marczak, R.J., (2018) Adomian decomposition method applied to laminated thick plates in bending, ZAMM Journal of Applied Mathematics and Mechanics, 2018, Vol. 99(2), e201800151, January 2019 https://doi.org/10.1002/zamm.201800151
  10. Jaradat, A.K., Obeidat1, A.A., Gharaibeh1, M.A., Qaseer, M.K.H., Adomian Decomposition Approach to Solve the Simple Harmonic Quantum Oscillator, International Journal of Applied Engineering Research, 2018, Volume 13, Number 2 (2018) pp. 1056-1059.
  11. Mao X. and Mao Q., A new aftertreatment for improving adomian modified decomposition method for solving nonlinear differential equations, Journal of Physics: Conference Series (Open Access), 2018, 1053, doi:10.1088/1742-6596/1053/1/012019
  12. Qasim, A.F., AL-Rawi, E., Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations, Journal of Applied Mathematics, Volume 2018, Article ID 1803107, https://doi.org/10.1155/2018/1803107
  13. Razmjooy, N., Ramezani, M., Solution of the Hamilton jacobi bellman uncertainties by the interval version of adomian decomposition method, International Robotics & Automation Journal, 2018, Volume 4, Issue 2.
  14. Yousef, H.M. and Ismail, A.I.B, Application of the Laplace Adomian decomposition method for solution system of delay differential equations with initial value problem, AIP Conference Proceedings, Vol. 1974, 020038 (2018); https://doi.org/10.1063/1.5041569

Reference List for ADM, 2019

  1. Alderremy, A.A., Elzaki, T.M., Chamekh, M., Modified Adomian Decomposition Method to Solve Generalized Emden–Fowler Systems for Singular IVP, Mathematical Problems in Engineering, 2019, Volume 2019, Article ID 6097095, 6 pages https://doi.org/10.1155/2019/6097095
  2. Ali, N., Ahmad, S., Aziz, S., Zaman, G., The Adomian decomposition method for solving HIV infection Model of latently infected cells, Matrix Science Mathematics (MSMK), 2019, http://doi.org/10.26480/msmk.01.2019.05.08
  3. Bakodah, H.O., Al-Mazmumy, M., Almuhalbedi, S.O., Abdullah, A., Solving system of integro differential equations using discrete adomian decomposition method, Journal of Taibah University for Science, 2019, Vol. 13, No. 1, pp. 805--812; https://doi.org/10.1080/16583655.2019.1625189
  4. Bakodah, H.O., Al-Mazmumy, M., Almuhalbedi, S.O., Abdullah, A., Laplace Discrete Adomian Decomposition Method for Solving Nonlinear Integro Differential Equations, Journal of Applied Mathematics and Physics, 2019, Vol.7, No.6, pp. 1388--1407. doi: 10.4236/jamp.2019.76093
  5. Fatoorehchi, H., Alidadi, M., Rach, R., and Shojaeian, A., Theoretical and Experimental Investigation of Thermal Dynamics of Steinhart–Hart Negative Temperature Coefficient Thermistors, ASME Journal of Heat Transfer, 2019, Vol. 141, Issue 7, 11 pages; Paper No: HT-18-1744; doi: 10.1115/1.4043676
  6. Gbenga, O., Approximate Solution of Eckhaus Equation Using Elzaki Decomposition Method, ASME: Journal of Heat Transfer (The American Society of Mechanical Engineers), 2019, Vol. 141, No. 7, 11 pages; doi: 10.1115/1.4043676
  7. González-Gaxiola, O., Numerical solution for Triki-Biswas equation by Adomian decomposition method, Optik - International Journal for Light and Electron Optics, October 2019, Vol. 194, 163014; https://doi.org/10.1016/j.ijleo.2019.163014
  8. González-Gaxiola, O., Biswas, A., Belic, M.R., Optical solution pertubabion of Fokas--Lenells equation by the Laplace--Adomian decomposition algorithm, Journal of the European Optical Society-Rapid, 2019, Vol. 15, No. pp. 1--9; https://doi.org/10.1186/s41476-019-0111-6
  9. González-Gaxiola, O., Chacón-Acosta, G., León-Ramírez, A., Approximate Analytical Solution of the Nonlinear Bethe Equation, International Journal of Applied and Computational Mathematics, 2019, 5:25. https://doi.org/10.1007/s40819-019-0616-0
  10. Goyal, K., Singhal, M., Adomian decomposition method for thermal analysis of a furnace, Pages 141-148, in: Advances in Engineering Research and Application: Proceedings of the International Conference, ICERA 2018, Lecture Notes in Networks and Systems, vol 63, edited by Hamido Fujita, Duy Cuong Nguyen, Ngoc Pi Vu, Tien Long Banh, Hermann Horst Puta, Springer Nature Switzerland AG, 2019.
  11. Guo, P., The Adomian decomposition method for a type of fractional differential equations, Journal of Applied Mathematics and Physics, Vol. 7, 2019, Pp. 2459-2466. https://doi.org/10.4236/jamp.2019.710166
  12. Gupta, S., Kumar, D., Singh, J., ADMP - A Maple Package for Symbolic Computation and Error Estimating to Singular Two-Point Boundary Value Problems with Initial Conditions, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, June 2019, Volume 89, Issue 2, pp 405–414. https://doi.org/10.1007/s40010-018-0540-4
  13. Hamoud, A.A., Mohammed, N.M., Ghadle, K.P., Dhondge, S.L., Solving Integro-Differential Equations by Using NumericalTechniques, International Journal of Applied Engineering Research, 2019, Volume 14, Number 14, (2019) pp. 3219-3225.
  14. Hussain, K.H., Some New Modifications of Adomian Technique forNonlinear Volterra Integral Equations, Int. J. Math. And Appl., 2019, Vol. 7, No. 1, pp. 9--14.
  15. Ige, O.E., Heilio, M., Oderinu, R.A., Elzaki, T.M., Adomian Polynomial and Elzaki Transform Method ofSolving Third Order Korteweg-De Vries Equations, Global Journal of Pure and Applied Mathematics, 2019, Volume 15, Number 3, pp. 261--277. 2019,
  16. Kaliyappan, M. and Hariharan, S., Solving nonlinear differential equations using Adomian decomposition method through Sagemath, International Journal of Innovative Technology and Exploring Engineering, 2019, Volume 8, Issue 6, pp. 510--515, April 2019
  17. Kasumo, C., Solving the linear homogeneous one-dimensional wave equation using the Adomian decomposition method, Applied Mathematical Sciences, 2019, Vol. 13, No. 5, 2019, pp. 239--252. https://doi.org/10.12988/ams.2019.9120
  18. Li, J., Wu, A., “Influence of non-ideal factors on the boundary control of buck converters with curved switching surfaces”, IEEE Access”, Volume 7, Pages 52790 - 52803, 2019, INSPEC Accession Number: 18621010, doi: 10.1109/ACCESS.2019.2912449.
  19. Lichae, B.H., Biazar, J., and Ayati, Z., The Fractional Differential Model of HIV-1 Infection of CD4 + T-Cells with Description of the Effect of Antiviral Drug Treatment, Hindawi Computational and Mathematical Methods in Medicine, 2019, Volume 2019, Article ID 4059549, 12 pages; https://doi.org/10.1155/2019/4059549
  20. Lin, Y., Jin, X., Chen J., Sodhro, A.H., Pan, Z., “An analytic computation-driven algorithm for Decentralized Multicore Systems”, Future Generation Computer Systems, 2019, Volume 96, July 2019, Pages 101-110; https://doi.org/10.1016/j.future.2019.01.031
  21. Lisbôa, T.V., Zhang, Ch., Marczak, R.J., “A modified decomposition method to solve linear elliptic partial differential equations in anisotropic domains by enhancing isotropic responses”, Meccanica, January 2019, Volume 54, Issue 1–2, pp 239–26; https://doi.org/10.1007/s11012-018-00933-w
  22. Moore, T.J., Ertürk, V.S., Comparison of the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems in engineering, Nonlinear Engineering, Vol.9, No. 1, 2019, pp. 1-13. https://doi.org/10.1515/nleng-2018-0148
  23. Raslan, K.R., Ali, K.K., Adomian decomposition method (ADM) for solving the nonlinear generalized regularized long wave equation, Numerical and Computational Methods in Science & Engineering, 2019, Vol. 1, No. 1, pp. 41--55.
  24. Shapovalov, A.V. and Trifonov, A.Yu., Adomian decomposition method for the one-dimensional nonlocal Fisher--Kolmogorov--Petrovsky--Piskunov equation, Russina Physics Journal, 2019, Vol. 62, No. 4, pp. 710--719; doi: 10.1007/s11182-019-01768-y
  25. Shapovalov, A.V. and Trifonov, A.Yu., Adomyan Decomposition Method for a Two-Component Nonlocal Reaction-Diffusion Model of the Fisher–Kolmogorov–Petrovsky–Piskunov Type, Russina Physics Journal, 2019, Vol. 62, No. 5, pp. 1--13; doi: 10.1007/s11182-019-01785-x
  26. Yun, Y.-S., Wen, Y., Temuer, C., Rach, R., A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area, Advances in Difference Equations, 2019, Article number 2019:438; https://doi.org/10.1186/s13662-019-23

Reference List for ADM, 2020

  1. Adair, D., Nagimova, A., Jaeger, M., Effect of thrust on the structural vibrations of a nonuniform slender rocket, Math. Comput. Appl. 2020, 25, 29; doi:10.3390/mca25020029
  2. Harko, T., Mak, M.K., Leung, C.S., Vortex solutions in atomic Bose-Einstein condensates via the Adomian decomposition method, arXiv:2003.04277v1 [Condensed Matter - Quantum Gases] 09 Mar 2020.
  3. Malaikah, H.M., The Adomian Decomposition Method for Solving Volterra--Fredholm Integral Equation using Maple, Applied Mathematics, 2020, 11, pp. 779--787; https://www.scirp.org/journal/am
  4. R. Rach, J.-S. Duan, A.-M. Wazwaz, Simulation of large deflections of a flexible cantilever beam fabricated from functionally graded materials by the Adomian decomposition method, International Journal of Dynamical Systems and Differential Equations, Vol. 10, No. 4, 2020, Pp. 287-298, Article ID 109104. DOI: 10.1504/IJDSDE.2020.109104. https://urldefense.proofpoint.com/v2/url?u=https-3A__www.inderscience.com_info_inarticle.php-3Fartid-3D109104&d=DwIBaQ&c=dWz0sRZOjEnYSN4E4J0dug&r=pVWny0Qg-9YwiqSyn-cCTA&m=qD9VWqAA4oLmDVvI6TbI7Lc3q8-vKxzHUwHpjoUjYCI&s=aebNvMp9yK1VaMLjBrAOYXedrAhC8pqz_0Y8Ua22XnQ&e=
  5. Vellaisamy, P. and Viens, F. (2020). A probabilistic approach to Adomian polynomials, Stochastic Analysis and Applications, 2020, 38, No. 6, pp. 1045-1062.

Reference List for ADM, 2021

  1. L. Bougoffa, R. Rach, A, Mennouni, On the existence, uniqueness, and new analytic approximation of the modified error function in two-phase Stefan problems, Mathematical Methods in the Applied Sciences, Volume 44, Issue 14, 30 September 2021, Pages 10948-10956
  2. J.-S. Duan, R. Rach, A.-M. Wazwaz, Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method, International Journal for Computational Methods in Engineering Science and Mechanics, 2021, https://doi.org/10.1080/15502287.2021.1904461.
  3. H. Fatoorehchi, R. Rach, Decomposition solution for a nonlinear model describing the diffusional growth of intermetallic layers, Acta Physica Polonica A, Vol. 140, No. 1, July 2021, Pages 91-96.
  5. Lu, T.-T. and Zheng, W.-Q., Adomian decomposition method for first order PDEs with unprescribed data, Alexandria Engineering Journal, 2021, Vol. 60, pp. 2563--2572.
  6. Mak, M.K., Leung, C.S., Harko, T., A brief Introduction to the Adomian Decomposition Method, with applications in Astronomy and Astrophysics, 2021, arXiv:2102.10511
  7. Maturi, D.A,m Malaikah, M., The Adomian decomposition method for solving nonlinear partial differential equation using Maple, Advances in Pure Mathematics, 2021, 11, pp. 595--603. https://www.scirp.org/journal/apm
  8. Mbagwu, JP.C. and Nwamba, J.I., Series solution of nonlinear ordinary differential equations using single Laplace transform method in mathematical physics, World Scientific News. An Intenational Scientific Journal, 2021, Vol. 154, pp. 152--174.
  9. Mohammed, P.O.; Machado, J.A.T.; Guirao, J.L.G.; Agarwal, R.P. Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations. Mathematics, 2021, 9, 1070. https://doi.org/10.3390/math9091070

Reference List for ADM, 2022

  1. Vellaisamy, P. and Kumar, V. A probabilistic interpretation of nonclassic Adomian polynomials. Stochastic Analysis and Applications, https://doi.org/10.1080/07362994.2021.1971539