Preface

This tutorial was made solely for the purpose of education and it was designed for students taking Applied Math 0330. It is primarily for students who have very little experience or have never used Mathematica and programming before and would like to learn more of the basics for this computer algebra system. As a friendly reminder, don't forget to clear variables in use and/or the kernel. The Mathematica commands in this tutorial are all written in bold black font, while Mathematica output is in normal font.

Finally, you can copy and paste all commands into your Mathematica notebook, change the parameters, and run them because the tutorial is under the terms of the GNU General Public License (GPL). You, as the user, are free to use the scripts for your needs to learn the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. The tutorial accompanies the textbook Applied Differential Equations. The Primary Course by Vladimir Dobrushkin, CRC Press, 2015; http://www.crcpress.com/product/isbn/9781439851043

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Glossary

Complete List of Publications for 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. Kansari Haldar, Decomposition Analysis Method in Linear and Nonlinear Differential Equations, Chapman and Hall/CRC, 2015.
  13. Serrano, S.E. (1997), Hydrology for Engineers, Geologists and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, HydroScience Inc., Lexington, KY.
  14. 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.
  15. Abdelrazec, A. (2008), Adomian decomposition method: convergence analysis and numerical approximations, MSc thesis (Mathematics), McMaster University, Hamilton, Ontario, Canada, November 2008.
  16. 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.
  17. 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.
  18. Serrano, S.E. (2016), Differential Equations: Applied Mathematical Modeling, Nonlinear Analysis, and Computer Simulation in Engineering and Science, HydroScience Inc., Ambler, Pennsylvania.
  19. Shingareva, I. and Lizárraga-Celaya, C. (2011), Solving Nonlinear Partial Differential Equations with Maple and Mathematica, Springer, New York, NY, pp. 227--242.
  22. Hamzah Faisal Tomaizeh, Modified Adomian Decomposition Method For Differential Equations, Ph D Thesis, 2017.
  23. Wazwaz, A.-M. (1997), A First Course in Integral Equations, World Scientific Publishing Co., Singapore and River Edge, NJ.
  24. Wazwaz, A.-M. (2002), Partial Differential Equations: Methods and Applications, A.A. Balkema, Lisse.
  25. Wazwaz, A.-M. (2009), Partial Differential Equations and Solitary Waves Theory, Higher Education Press, Beijing, and Springer, Berlin.
  26. Wazwaz, A.-M. (2011), Linear and Nonlinear Integral Equations: Methods and Applications, Higher Education Press, Beijing and Springer, Berlin.

A bibliography of the theory and applications of the ADM

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

Reference List for ADM, 1965

Reference List for ADM, 1966

Reference List for ADM, 1967

Reference List for ADM, 1968

Reference List for ADM, 1969

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.

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.
  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.

Reference List for ADM, 1973

Reference List for ADM, 1974

Reference List for ADM, 1975

Reference List for ADM, 1976

  1. Adomian, G., “Nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, 1976, Vol. 55, No. 2, pp. 441--452.

Reference List for ADM, 1977

  1. 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.
  2. 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.

Reference List for ADM, 1979

  1. 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.

Reference List for ADM, 1980

  1. 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.
  2. 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.
  3. 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.
  4. Adomian, G. and Malakian, K., “Stochastic analysis”, Mathematical Modelling, 1980, Vol. 1, No. 3, pp. 211--235.
  5. 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. and Bellman, R.E., “On the Itô equation”, Journal of Mathematical Analysis and Applications, 1982, Vol. 86, No. 2, pp. 476--478.
  6. 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.
  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.
  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.

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. G. Adomian and R. Rach, 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.
  13. Adomian, G. and Rach, R., “Nonlinear differential equations with negative power nonlinearities”, Journal of Mathematical Analysis and Applications, 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.
  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.
  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.

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.
  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.
  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, doi: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.
  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.
  18. Adomian, G. and Rach, R., “A coupled nonlinear system”, Journal of Mathematical Analysis and Applications, 1986, Vol. 113, No. 2, pp. 510--513.
  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.
  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, Vol. 113, No. 1, pp. 199--201.
  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.
  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.
  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. 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.
  15. 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.
  16. 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.

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.
  18. 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.

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.

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.
  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.
  11. Baghdasarian, A., “Comments on the validity of a proposed counterexample on the method of decomposition”, Mechanics Research Communications, 1990, Vol. 18, No. 1, pp. 67--69.

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.
  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.

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, Vol. 18, No. 12, pp. 103--106.

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.
  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.
  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.
  4. Adomian, G., “Solution of nonlinear evolution equations”, Mathematical and Computer Modelling, 1994, Vol. 20, No. 12, pp. 1--2.
  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.

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.

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, 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.

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.
  9. Diţă, P. and Grama, N. (1997), On Adomian’s decomposition method for solving differential equations, Preprint.

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.
  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.

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.
  5. Golberg, M.A., "A note on the decomposition method for operator equation," Applied Mathematics and Computation, 1999, 106, 215--220.

Reference List for ADM, 2000

  1. Babolian, E. and Biazar, J., Solution of a system of nonlinear Volterra integral equations of the second kind, Far East Journal of Mathematical Sciences, 2000, Vol. 2, No. 6, pp. 935--945.
  2. 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.
  3. 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.
  4. 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.

Reference List for ADM, 2001

  1. Abbaoui, K., Pujol, M.J., Cherruault, Y., Himoun, N., and Grimalt, P., “A new formulation of Adomian method: convergence result”, Kybernetes, 2001, Vol. 30, Nos 9/10, pp. 1183--1191.
  2. 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), was available at: www.ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/ccd=GFzW1p/record?r1=1&h1=2.

Reference List for ADM, 2002

  1. Babolian, E. and Biazar, J., “On the order of convergence of Adomian method”, Applied Mathematics and Computation, 2002, Vol. 130, Nos. 2/3, pp. 383--387.
  2. Babolian, E. and Biazar, J., “Solution of nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, 2002, Vol. 132, No. 1, pp. 167--172.
  3. Babolian, E. and Biazar, J., “Solving the problem of biological species living together by Adomian decomposition method”, Applied Mathematics and Computation, 2002, Vol. 129, Nos 2/3, pp. 339--343.
  4. Bulut, H. and Evans, D.J., “On the solution of the Riccati equation by the decomposition method”, International Journal of Computer Mathematics, 2002, Vol. 79, No. 1, pp. 103--109.
  5. Casasús, L. and Al-Hayani, W., “The decomposition method for ordinary differential equations with discontinuities”, Applied Mathematics and Computation, 2002, Vol. 131, Nos 2/3, pp. 245--251.
  6. Chiu, C.-H. and Chen, C.-K. (2002a), “A decomposition method for solving the convective longitudinal fins with variable thermal conductivity”, International Journal of Heat and Mass Transfer, Vol. 45 No. 10, pp. 2067-75.
  7. Chiu, C.-H. and Chen, C.-K. (2002b), “Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity”, Acta Mechanica, Vol. 157 Nos 1/4, pp. 147-58.
  8. Chiu, C.-H. and Chen, C.-K., “Thermal stresses in annular fins with temperature-dependent conductivity under periodic boundary condition”, Journal of Thermal Stresses, 2002, Vol. 25, pp. 475--492.
  9. Chrysos, M., Sanchez, F. and Cherruault, Y. (2002), “Improvement of convergence of Adomian’s method using Padé approximants”, Kybernetes, Vol. 31, No. 6, pp. 884--895.
  10. Deeba, E.Y., Dibeh, G., and Xie, S., “An algorithm for solving bond pricing problem”, Applied Mathematics and Computation, 2002, Vol. 128, No. 1, pp. 81--94.
  11. Deeba, E.Y., Yoon, J.-M., “A decomposition method for solving nonlinear systems of compartment models”, Journal of Mathematical Analysis and Applications, 2002, Vol. 266, No. 1, pp. 227--236.

Reference List for ADM, 2003

  1. Abbasbandy, S., “Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, 2003, Vol. 145, Nos. 2/3, pp. 887--893.
  2. Babolian, E. and Biazar, J., “Solving concrete examples by Adomian method”, Applied Mathematics and Computation, 2003, Vol. 135, No. 1, pp. 161--167.
  3. Babolian, E. and Javadi, Sh., “Restarted Adomian method for algebraic equations”, Applied Mathematics and Computation, 2003, Vol. 146, Nos 2/3, pp. 533--541.
  4. Biazar, J., Babolian, E., and Islam, R., Solution of a system of Volterra integral equations of the first kind by Adomian method, Applied Mathematics and Computation, Vol. 139, No. , pp. 249--258.
  5. Biazar, J., Babolian, E., Kember, G., Nouri, A., and Islam, R., An alternate algorithm for computing Adomian polynomials in special cases, Applied Mathematics and Computation, Vol. 138, Nos 2/3, pp. 523--529.
  6. Biazar, J., Tango, M., Babolian, E., and Islam, R., “Solution of the kinetic modeling of lactic acid fermentation using Adomian decomposition method”, Applied Mathematics and Computation, 2003, Vol. 144, Nos 2/3, pp. 433--439.
  7. Bulut, H. and Evans, D.J., “Oscillations of solutions of initial value problems for parabolic equations by the decomposition method”, International Journal of Computer Mathematics, 2003, Vol. 80, No. 7, pp. 863--868.
  8. Chiu, C.-H. and Chen, C.-K. (2003), “Application of Adomian’s decomposition procedure to the analysis of convective-radiative fins”, Journal of Heat Transfer, Vol. 125, pp. 312--316.
  9. Choi, H.-W. and Shin, J.-G. (2003), “Symbolic implementation of the algorithm for calculating Adomian polynomials”, Applied Mathematics and Computation, Vol. 146, No. 1, pp. 257--271.

Reference List for ADM, 2004

  1. Al-Khaled, K. and Allan, F., “Construction of solutions for the shallow water equations by the decomposition method”, Mathematics and Computers in Simulation, 2004, Vol. 66, No. 6, pp. 479--486.
  2. Al-Khaled, K., Kaya, D., and Noor, M.A., “Numerical comparison of methods for solving parabolic equations”, Applied Mathematics and Computation, 2004, Vol. 157, No. 3, pp. 735--43.
  3. Asil, V., Bulut, H., and Evans, D.J., “On the oscillatory solutions of nonlinear hyperbolic differential equations by the decomposition method”, International Journal of Computer Mathematics, 2004, Vol. 81, No. 5, pp. 639--645.
  4. Babolian, E., Biazar, J., and Vahidi, A.R., “A new computational method for Laplace transforms by decomposition method”, Applied Mathematics and Computation, 2004, Vol. 150, No. 3, pp. 841--846.
  5. Babolian, E., Biazar, J., and Vahidi, A.R., “Solution of a system of nonlinear equations by Adomian decomposition method”, Applied Mathematics and Computation, 2004, Vol. 150, No. 3, pp. 847--854.
  6. Babolian, E., Biazar, J. and Vahidi, A.R., “The decomposition method applied to systems of Fredholm integral equations of the second kind”, Applied Mathematics and Computation, 2004, Vol. 148, No. 2, pp. 443--452.
  7. Babolian, E. and Davari, A., “Numerical implementation of Adomian decomposition method”, Applied Mathematics and Computation, 2004, Vol. 153, No. 1, pp. 301--305.
  8. Babolian, E. and Javadi, Sh., “New method for calculating Adomian polynomials”, Applied Mathematics and Computation, 2004, Vol. 153, No. 1, pp. 253--259.
  9. Babolian, E., Javadi, Sh., and Sadeghi, H., “Restarted Adomian method for integral equations”, Applied Mathematics and Computation, 2004, Vol. 153, No. 2, pp. 353--359.
  10. Babolian, E., Sadeghi, H., and Javadi, Sh., “Numerically solution of fuzzy differential equations by Adomian method”, Applied Mathematics and Computation, 2004, Vol. 149, No. 2, pp. 547--557.
  11. Benabidallah, M. and Cherruault, Y., “Application of the Adomian method for solving a class of boundary problems”, Kybernetes, 2004, Vol. 33, No. 1, pp. 118--132.
  12. Benabidallah, M. and Cherruault, Y., “Solving a class of linear partial differential equations with Dirichlet-boundary conditions by the Adomian method”, Kybernetes, 2004, Vol. 33, No. 8, pp. 1292--1311.
  13. Benabidallah, M. and Cherruault, Y., “Using the Adomian method for solving a class of boundary differential systems”, Kybernetes, 2004, Vol. 33, No. 7, pp. 1185--1204.
  14. Bhattacharyya, R.K. and Bera, R.K., “Application of Adomian method on the solution of the elastic wave propagation in elastic bars of finite length with randomly and linearly varying Young’s modulus”, Applied Mathematics Letters, 2004, Vol. 17, No. 6, pp. 703--709.
  15. Biazar, J., Babolian, E., and Islam, R., “Solution of the system of ordinary differential equations by Adomian decomposition method”, Applied Mathematics and Computation, 2004, Vol. 147, No. 3, pp. 713--719.
  16. Biazar, J. and Islam, R., “Solution of wave equation by Adomian decomposition method and the restrictions of the method”, Applied Mathematics and Computation, 2004, Vol. 149, No. 3, pp. 807--814.
  17. Boumenir, A. and Gordon, M., “The rate of convergence for the decomposition method,” Numerical Functional Analysis and Optimization, 2004, Vol. 25, Nos 1/2, pp. 15--25.
  18. 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”, Applied Mathematics and Computation, 2004, Vol. 153, No. 3, pp. 733--741.
  19. Chen, W. and Lu, Z. (2004), “An algorithm for Adomian decomposition method”, Applied Mathematics and Computation, 2004, Vol. 159, No. 1, pp. 221--235.
  20. Dehghan, M., “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.
  21. Dehghan, M., “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.
  22. Dehghan, M. (2004c), “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.

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.
  2. Abbasbandy, S. and Darvishi, M.T., “A numerical solution of Burgers’ equation by modified Adomian method”, Applied Mathematics and Computation, 2005, Vol. 163, No. 3, pp. 1265--1272.
  3. Abbasbandy, S. and Darvishi, M.T., “A numerical solution of Burgers’ equation by time discretization of Adomian’s decomposition method”, Applied Mathematics and Computation, 2005, Vol. 170, No. 1, pp. 95--102.
  4. Al-Hayani, W. and Casasús, L., “Approximate analytical solution of fourth order boundary value problems”, Numerical Algorithms, 2005, Vol. 40, No. 1, pp. 67--78.
  5. Al-Hayani, W. and Casasús, L., “The Adomian decomposition method in turning point problems”, Journal of Computational and Applied Mathematics, 2005, Vol. 177, No. 1, pp. 187--203.
  6. Arslanturk, C., “A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity”, International Communications in Heat and Mass Transfer, 2005, Vol. 32, No. 6, pp. 831--41.
  7. Asil, V., Bulut, H., and Evans, D.J., “The Adomian decomposition method for the approximate solution of homogeneous differential equations with dual variable and dual coefficients”, International Journal of Computer Mathematics, 2005, Vol. 82, No. 8, pp. 977--986.
  8. Attili, B.S., “The Adomian decomposition method for computing eigenelements of Sturm-Liouville two point boundary value problems”, Applied Mathematics and Computation, 2005, Vol. 168, No. 2, pp. 1306--1316.
  9. Babolian, E. and Davari, A., “Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind”, Applied Mathematics and Computation, 2005, Vol. 165, No. 1, pp. 223--227.
  10. Babolian, E., Goghary, H.S., Javadi, Sh., and Ghasemi, M., “Restarted Adomian method for nonlinear differential equations”, International Journal of Computer Mathematics, Vol. 82, No. 1, pp. 97--102.
  11. Babolian, E., Vahidi, A.R., and Cordshooli, Gh.A., “Solving differential equations by decomposition method”, Applied Mathematics and Computation, 2005, Vol. 167, No. 2, pp. 1150--1155.
  12. Benneouala, T., Cherruault, Y. and Abbaoui, K., “New methods for applying the Adomian method to partial differential equations with boundary conditions”, Kybernetes, 2005, Vol. 34, Nos. 7/8, pp. 924--933.
  13. Biazar, J., “Solution of systems of integral-differential equations by Adomian decomposition method”, Applied Mathematics and Computation, 2005, Vol. 168, No. 2, pp. 1232--1238.
  14. Biazar, J. and Amirtaimoori, A.R., “An analytic approximation to the solution of heat equation by Adomian decomposition method and restrictions of the method”, Applied Mathematics and Computation, 2005, Vol. 171, No. 2, pp. 738--745.
  15. Biazar, J. and Ebrahimi, H., “An approximation to the solution of hyperbolic equations by Adomian decomposition method and comparison with characteristics method”, Applied Mathematics and Computation, 2005, Vol. 163, No. 2, pp. 633--638.
  16. Biazar, J. Ilie, M., Khoshkenar, A., An improvement to an alternate algorithm for computing Adomian polynomials in special cases, 2005, pp.
  17. Cafagna, D. and Grassi, G. (2005), Adomian decomposition method as a tool for numerical studying multi-scroll hyperchaotic attractors, 2005 International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Bruges, Belgium, October 18-21, 2005, pp. 505--508.
  18. Chun, C. (2005), “Iterative methods improving Newton’s method by the decomposition method”, Computers and Mathematics with Applications, Vol. 50, Nos 10/12, pp. 1559--1568.
  19. Copetti, M.I.M., Krein, G., Machado, J.M. and Marques de Carvalho, R.S. (2005), “Studying nonlinear effects on the early stage of phase ordering using a decomposition method”, Physics Letters A, Vol. 338, Nos 3/5, pp. 232--238.
  20. Daftardar-Gejji, V. and Jafari, H., “Adomian decomposition: a tool for solving a system of fractional differential equations”, Journal of Mathematical Analysis and Applications, 2005, Vol. 301, No. 2, pp. 508--518.
  21. Dehghan, M. and Tatari, M. (2005), “Solution of a parabolic equation with a time-dependent coefficient and an extra measurement using the decomposition procedure of Adomian”, Physica Scripta, 2005, Vol. 72, No. 6, pp. 425--431.
  22. Goghary, H.S., Javadi, Sh., Babolian, E., Restarted Adomian method for system of nonlinear Volterra integral equations, Applied Mathematics and Computation, 2005, Vol. 161, pp. 745--751.

Reference List for ADM, 2006

  1. Abbasbandy, S., Numerical solution of the integral equations: Homotopy perturbation method and Adomian decomposition method, Applied Mathematics and Computation, 2006, Vol. 173, pp. 393--500.
  2. 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.
  3. 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.
  4. 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.
  5. Biazar, J. (2006), “Solution of the epidemic model by Adomian decomposition method”, Applied Mathematics and Computation, Vol. 173 No. 2, pp. 1101-6.
  6. 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.
  7. 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.
  8. 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.
  9. Biazar, J. and Pourabd, M., A Maple program for computing Adomian polynomials, International Mathematical Forum, 2006, Vol. 1 No. 39, pp. 1919--1924 .
  10. Bildik, N. and Konuralp, A., Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations, International Joirnal of Computer Mathematics, 2006, Vol. 83, Issue 12, pp. 973--987; https://doi.org/10.1080/00207160601173407
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Chun, C. (2006), “A new iterative method for solving nonlinear equations”, Applied Mathematics and Computation, Vol. 178, No. 2, pp. 415--422.
  16. 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.
  17. Daftardar-Gejji, V. and Jafari, H., “Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition”, Applied Mathematics and Computation, 2006, Vol. 180, No. 2, pp. 488--497.
  18. 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
  19. 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.
  21. Lesnic, D., Blow-up solutions obtained using the decomposition method, Chaos, Solitons and Fractals, Vol. 28, (2006) 776--787.

Reference List for ADM, 2007

  1. 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.
  2. 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, Vol. 2, No. 2, pp. 87--96.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.

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. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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
  13. Dită, P. and Grama, N., On Adamian's decomposition method for solving differential equations, Institute of Atomic Physics, Bucharest, 2008.
  14. 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.
  15. 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. https://doi.org/10.1016/j.aml.2007.05.008

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. 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.
  5. 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.
  6. Aslanov, A., “Approximate solutions of Emden-Fowler type equations”, International Journal of Computer Mathematics, 2009, Vol. 86, No. 5, pp. 807--826.
  7. 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.
  8. 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.
  9. 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.
  10. 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
  11. Bohner, M. and Zheng, Y., “On analytical solutions of the Black-Scholes equation”, Applied Mathematics Letters, 2009, Vol. 22, No. 3, pp. 309--313.
  12. 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.
  13. 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.
  14. 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, Vol. 14, No. 4, pp. 1008--1012.
  15. 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.
  16. 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.
  17. 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.

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, 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.
  14. 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.
  15. 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.
  16. Duan, J.-S., Recurrence triangle for Adomian polynomials, Applied Mathematics and Computation, 2010, Vol. 216, No. 4, pp. 1235--1241.
  17. Duan, J.-S., “An efficient algorithm for the multivariable Adomian polynomials”, Applied Mathematics and Computation, 2010, Vol. 217, No. 6, pp. 2456--2467.
  18. Duan, J.-S. and Guo, A.-P. (2010), “Reduced polynomials and their generation in Adomian decomposition methods”, Computer Modeling in Engineering and Sciences, Vol. 60 No. 2, pp. 139--150. doi: 10.3970/cmes.2010.060.139
  19. 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.
  20. 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.
  21. 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
  22. 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.
  23. 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, Vol. 59 No. 5, pp. 1759--1765.
  24. 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, Vol. 6 No. 4, pp. 38-52, available at: www.ijamm.bc.cityu.edu.hk/ijamm/outbox/Y2010V6N4P38C2112979.pdf
  25. 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.

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. A. Abdelrazec, D. Pelinovsky, Convergence of the Adomian decomposition method for initial-value problems, Numerical Methods for Partial Differential Equations, Vol. 27, No. 4, 749--766, 2011.
  3. 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.
  4. 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.
  5. 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.
  6. 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
  7. J.-S. Duan and R. Rach, New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods, Applied Mathematics and Computation, Volume 218, issue 6, 2011, 2810-2828.
  8. 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, Vol. 10, pp. 1718--1723.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. Duan, J.-S. (2011a), “Convenient analytic recurrence algorithms for the Adomian polynomials”, Applied Mathematics and Computation, Vol. 217 No. 13, pp. 6337-48.
  22. Duan, J.-S. (2011b), “New recurrence algorithms for the nonclassic Adomian polynomials”, Computers and Mathematics with Applications, Vol. 62 No. 8, pp. 2961-77.
  23. Duan, J.-S. (2011c), “New ideas for decomposing nonlinearities in differential equations”, Applied Mathematics and Computation, Vol. 218 No. 5, pp. 1774-84.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. Ebaid, A., “Approximate analytical solution of a nonlinear boundary value problem and its application in fluid mechanics”, Zeitschrift für Naturforschung A (Physical Sciences), 2011, Vol. 66a, Nos 6/7, pp. 423-6. available on the web
  29. 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.
  30. 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.
  32. Fatoorehchi, H. and Abolghasemi, H., On Calculation of Adomian Polynomials by MATLAB, Journal of Applied Computer Science & Mathematics, 2011, Vol. 5, Issue 2, pp.85--88.
  33. Ekaterina Kutafina. Taylor Series for Adomian Decomposition Method, International Journal of Computer Mathematics, Volume 88, 2011, Issue 17, Pages 3677--3684.

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. 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.
  3. 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
  4. 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
  5. Duan, J.-S. and Rach, R. (2012b), “On the domain of convergence of the Adomian series solution”, International Journal of Computer Mathematics
  6. Duan, J.-S., Rach, R. and Wazwaz, A.-M. (2012), “Solution of the nonlinear pull-in behavior in micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems”, Physica E: Low-dimensional Systems and Nanostructures,
  7. 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
  9. 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.

Reference List for ADM, 2013

  1. Waleed Al-Hayani, "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. J.-S. Duan, R. Rach, and Z. Wang, On the effective region of convergence of the decomposition series solution, Journal of Algorithms and Computational Technology, Volume 7, 2013, 227--247.
  3. J.-S. Duan, R. Rach, and A.-M. Wazwaz, A new modified Adomian decomposition method for higher-order nonlinear dynamical systems, CMES: Computer Modeling in Engineering & Sciences, Vol. 94, No. 1, 2013, pp. 77--118.
  4. 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
  5. Saeedi, L., Tari, A., Masuleh, H.M., Numerical Solution of Some Nonlinear Volterra Integral Equations of the First Kind, Applications and Applied Mathematics: An International Journal, 2013, Vol. 8, Issue 1, pp. 214--226.

Reference List for ADM, 2014

  1. 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
  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. Danish, M., Use of Adomian and Restarted Adomian Methods for Solving Algebraic Equations, Journal of Basic and Applied Engineering Research, 2014, Vol. 1, No. 10, pp. 76--78. http://www.krishisanskriti.org/jbaer.html
  4. 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, 95--109, doi 10.1007/s40314-013-0045-3
  5. H. Fatoorehchi, H. Abolghasemi, R. Rach, An accurate explicit form of the Hankinson--Thomas--Phillips correlation for prediction of the natural gas compressibility factor, Journal of Petroleum Science and Engineering, Volume 117, May 2014, pp. 46--53.
  6. H. Fatoorehchi, H. Abolghasemi, R. Rach, M. Assar, An improved algorithm for calculation of the natural gas compressibility factor via the Hall-Yarborough equation of state, The Canadian Journal of Chemical Engineering, Volume 92, Issue 12, 2014, pp. 2211--2217.
  7. Salih Yalçınbaş and Dilek Taştekin, "Fermat Collocation Method for Solvıng a Class of the Second Order Nonlinear Differential Equations," Applied Mathematics and Physics, 2014, Vol 2, No 2, pp. 33--39, doi: 10.12691/amp-2-2-2
  8. 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
  9. H. Jafari, E. Tayyebi1, S. Sadeghi, C. M. Khalique, A new modification of the Adomian decomposition method for nonlinear integral equations, Int. J. Adv. Appl. Math, and Mech. 1(4) (2014) 33 – 39.

Reference List for ADM, 2015

  1. Agom, E.U. and Ogunfiditimi, F.O., Modified Adomian Polynomial for Nonlinear Functional with Integer Exponent, IOSR Journal of Mathematics, 2015, Vol. 11, Issue 6, Ver. V, pp. 40--45.
  2. Biazar, J. and Didgar, M., Numerical solution of Riccati equations by the Adomian and asymptotic decomposition methods over extended domains, International Journal of Differential Equations, Volume 2015, Article ID 580741, 7 pages http://dx.doi.org/10.1155/2015/580741
  3. J.-S. Duan and R. Rach, The degenerate form of the Adomian polynomials in the power series method for nonlinear ordinary differential equations, Journal of Mathematics and System Science, Volume 5, Pages 411--428, doi: 10.17265/2159-5291/2015.10.003
  4. H. Fatoorehchi, H. Abolghasemi, and R. Rach, A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis-Menten type nonlinearities, Fluid Phase Equilibria, Vol. 395, 2015, pp. 44--50.
  5. H. Fatoorehchi, R. Rach, O. Tavakoli, and H. Abolghasemi, 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.
  6. I. Tabet, M. Kezzar, K. Touafek, N. Bellel, S. Gherieb, A. Khelifa, and M. Adouane, 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.

Reference List for ADM, 2016

  1. 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
  2. Gonzalez-Gaxiola, ). and Bernal-Jaquez, R., Applying Adomian decomposition method to solve Burgess equation with a non-linear source, 2016, Mexico.

Reference List for ADM, 2017

  1. Mariam Al-Mazmumy and Safa Otyuan Almuhalbedi, "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
  2. Hao, L, Xiaoyan, L, Song, L., Wei, J., Adomian's method applied to solve ordinary and partial fractional differential equations, Journal of Shanghai Jiaotong University (Science), 2017, Vol. 22, Issue 3, pp. 371--376; doi: 10.1007/s12204-017-1846-0
  3. 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

Reference List for ADM, 2018

  1. Abaoub, A.S., Shkheam, A.S., Zali, S.M., The Adomian Decomposition Method of Volterra Integral Equation of Second Kind, American Journal of Applied Mathematics, 2018, Vol. 6, No. 4, pp. 142-148. doi: 10.11648/j.ajam.20180604.12
  2. Béyi Boukary, Justin Loufouilou-Mouyedo, Joseph Bonazebi-Yindoula, and Gabriel Bissanga, "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

 

 

 

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