Computer-Aided Analysis of Difference Schemes for Partial Differential Equations

The Necessary Basics from the Stability Theory of DifferenceSchemes and Polynomials.

Symbolic-Numerical Method for the Stability Investigation ofDifference Schemes on a Computer.

Application of Optimization Methods to the Stability Analysis ofDifference Schemes.

Stability Analysis of Difference Schemes by Catastrophe TheoryMethods.

Construction of Multiply Connected Stability Regions of DifferenceSchemes by Computer Algebra and Pattern Recognition.

Maximally Stable Difference Schemes.

Stability Analysis of Nonlinear Difference Schemes.

Symbolic Computation of Differential Approximations.

Appendices.

Index.