# A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab

Cambridge University Press, 3/16/2009

EAN 9780521519861, ISBN10: 0521519861

Hardcover, 490 pages, 25.3 x 21.5 x 3.1 cm

Language: English

Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.

1. An introduction to the Method of Lines (MOL)

2. A one-dimensional, linear partial differential equation

3. Green's function analysis

4. Two nonlinear, variable coeffcient, inhomogeneous PDEs

5. Euler, Navier-Stokes and Burgers equations

6. The Cubic SchrÃƒÂ¶dinger Equation (CSE)

7. The Korteweg-deVries (KdV) equation

8. The linear wave equation

9. Maxwell's equations

10. Elliptic PDEs

Laplace's equation

11. Three-dimensional PDE

12. PDE with a mixed partial derivative

13. Simultaneous, nonlinear, 2D PDEs in cylindrical coordinates

14. Diffusion equation in spherical coordinates

Appendix 1

partial differential equations from conservation principles

the anisotropic diffusion equation

Appendix 2

order conditions for finite difference approximations

Appendix 3

analytical solution of nonlinear, traveling wave partial differential equations

Appendix 4

implementation of time varying boundary conditions

Appendix 5

the DSS library

Appendix 6

animating simulation results.