Numerical Solutions for Partial Differential Equations: Problem Solving Using Mathematica

Introduction to Mathematica General Information about Mathematica Symbolic Computations with Mathematica Numerical Computations with Mathematica Finite Difference Methods for Hyperbolic PDEs Construction of Difference Schemes for the Advection Equation The Notion of Approximation Fourier Stability Analysis Elementary Second-Order Schemes Algorithm for Automatic Determination of Approximation Order of Scalar Difference Schemes Monotonicity Property of Difference Schemes TVD Schemes The Construction of Difference Schemes for Systems of PDEs Implicit Difference Schemes Von Neumann Stability Analysis in the Case of Systems of Difference Equations Difference Initial- and Boundary-Value Problems Construction of Difference Schemes for Multidimensional Hyperbolic Problems Determination of Planar Stability Regions Curvilinear Spatial Grids Answers to the Exercises Finite Difference Methods for Parabolic PDEs Basic Types of Boundary Conditions for Parabolic PDEs Simple Schemes for the One-Dimensional Heat Equation Difference Schemes for Advection-Diffusion Equation Runge-Kutta Methods Finite Volume Method The Adi Method Approximate Factorization Scheme Dispersion Answers to the Exercises Numerical Methods for Elliptic PDEs Boundary-Value Problems for Elliptic PDEs A Simple Elliptic Solver Pseudo-Unsteady Methods The Finite Element Method Numerical Grid Generation Local Approximation Study of Finite Volume Operators on Arbitrary Grids Local Approximation Study of Difference Schemes on Logically Rectangular Grids Answers to the Exercises Appendix Glossary of Programs Index Each Chapter also includes a list of references.