A Compendium of Partial Differential Equation Models

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.

ISBN 0521519861   Pages 490 ISBN13 9780521519861 (What's this?)   Volumes 1 Publisher Cambridge University Press   Weight (grammes) 1100 Imprint Cambridge University Press   Published in Cambridge Format Hardback   Height (mm) 253 Publication date 16 Mar 2009   Width (mm) 215 Library of Congress 2008045816   Spine width (mm) 31 DEWEY 515.353   Academic level Undergraduate, Postgraduate, Professional / Scholarly DEWEY edition DC22

1		An Introduction to the Method of Lines		1
2		A One-Dimensional, Linear Partial Differential Equation		18
3		Green's Function Analysis		36
4		Two Nonlinear, Variable-Coefficient, Inhomogenous Partial Differential Equations		70
5		Euler, Navier Stokes, and Burgers Equations		90
6		The Cubic Schrodinger Equation		114
7		The Korteweg-deVries Equation		141
8		The Linear Wave Equation		171
9		Maxwell's Equations		203
10		Elliptic Partial Differential Equations: Laplace's Equation		229
11		Three-Dimensional Partial Differential Equation		261
12		Partial Differential Equation with a Mixed Partial Derivative		291
13		Simultaneous, Nonlinear, Two-Dimensional Partial Differential Equations in Cylindrical Coordinates		306
14		Diffusion Equation in Spherical Coordinates		342
Appendix 1		Partial Differential Equations from Conservation Principles: The Anisotrophic Diffusion Equation		381
Appendix 2		Order Conditions for Finite-Difference Approximations		398
Appendix 3		Analytical Solution of Nonlinear, Traveling Wave Partial Differential Equations		414
Appendix 4		Implementation of Time-Varying Boundary Conditions		420
Appendix 5		The Differentiation in Space Subroutines Library		441
Appendix 6		Animating Simulation Results		445
		Index		469

'The presented book is very interesting not only for students in applied mathematics, physics and engineering, but also for their teachers and can act as an effective and useful motivation in their work.' Zentralblatt MATH

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