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Computer-aided analysis of difference schemes for partial differential equations

Counter Advances in computer technology have conveniently coincided with trends in numerical analysis toward increased complexity of computational algorithms based on finite difference methods. It is no longer feasible to perform stability investigation of these methods manually--and no longer neces...

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Bibliographic Details
Main Author: Ganzha, Victor G.
Other Authors: Vorozhtsov, E. V
Format: Book
Language:English
Published: New York John Wiley & Sons 1996
Subjects:
Differential equations, Partial > Numerical solutions > Data processing.
Finite differences > Data processing.
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Table of Contents:
  • 1. The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials
  • 2. Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer
  • 3. Application of Optimization Methods to the Stability Analysis of Difference Schemes
  • 4. Stability Analysis of Difference Schemes by Catastrophe Theory Methods
  • 5. Construction of Multiply Connected Stability Regions of Difference Schemes by Computer Algebra and Pattern Recognition
  • 6. Maximally Stable Difference Schemes
  • 7. Stability Analysis of Nonlinear Difference Schemes
  • 8. Symbolic Computation of Differential Approximations
  • Appendix A. Gas-Dynamic Matrices
  • Appendix B. REDUCE Program for Scheme (4.6.19).

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