Description
Book SynopsisAdvances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically.
Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more.
Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Eq
Table of ContentsThe 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.
