Preface
Separation of variables is the basic mathod for solving linear partial differential equations (PDE for short). Not every linear PDE admits separation of variables and some classes of such equations are presented. Partial differential equations are usually suplemented by the initial and/or boundary conditions that reduces separation of variable further. This method could be extended to so called integrable evolution PDEs (linear or nonlinear) that can be written in the form of Lax pairs. For example, a classical diffusion equation \( u_t = \alpha\,u_{xx} \) can be decomposed into associated Lax pair consists of the following two linear equations
Return to computing page for the first course APMA0330
Return to computing page for the second course APMA0340
Return to Mathematica tutorial for the first course APMA0330
Return to Mathematica tutorial for the second course APMA0340
Return to the main page for the first course APMA0330
Return to the main page for the second course APMA0340
Return to Part VI of the course APMA0340
Introduction to Linear Algebra with Mathematica
Glossary
Separation of variables
- Costa, G. and Levine, L.E., Families of separable partial differential equations, International Journal of Mathematical Education in Science and Technology, 1993, Vol. 24, No. 5, pp. 621--635; doi: 10.1080/0020739930240503
- Fokas, A.S. and Spence, E.A., Synthesis, as opposed to separation of variables, SIAM Review, 2012, Vol. 54, No. 2, pp. 291--324.
Return to Mathematica page
Return to the main page (APMA0340)
Return to the Part 1 Matrix Algebra
Return to the Part 2 Linear Systems of Ordinary Differential Equations
Return to the Part 3 Non-linear Systems of Ordinary Differential Equations
Return to the Part 4 Numerical Methods
Return to the Part 5 Fourier Series
Return to the Part 6 Partial Differential Equations
Return to the Part 7 Special Functions