Computer-Aided Analysis of Difference Schemes for Partial Differential Equations / Edition 1

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Overview

A topical and comprehensive reference containing applications of computerized symbolic manipulations for analyzing the stability of a wide range of diverse schemes commonly used for solving problems in gas dynamics, catastrophe theory, heat and mass transfer. Provides basic mathematical formula for implementing each algorithm and all formulas are presented on a variety of computer operating systems using global algebraic symbolic languages such as MAPLE, MATHEMATICA and REDUCE. Features scores of illustrations and examples.
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Product Details

  • ISBN-13: 9780471129462
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 4/12/1996
  • Edition number: 1
  • Pages: 458
  • Product dimensions: 6.38 (w) x 9.57 (h) x 1.10 (d)

Meet the Author

VICTOR G. GANZHA is Visiting Professor of Mathematics with the Faculty of Mathematics and Informatics at the University of Kassel, Germany, where he presents lecture courses on advanced computer algebra systems and their applications to higher mathematics and numerical analysis. He is coauthor of Differentialgleichungen mit Mathematica.

E. V. VOROZHTSOV is a research scientist at the Russian Academy of Sciences in Novosibirsk, Russia, and Professor of Mathematics with the Faculty of Flying Vehicles at the Novosibirsk State Technical University. He is coauthor of Methods for the Localization of Singularities in Numerical Solutions of Gas Dynamics Problems.

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Table of Contents

Preface
1 The Necessary Basics from the Stability Theory of Difference Schemes and Polynomials 1
2 Symbolic-Numerical Method for the Stability Investigation of Difference Schemes on a Computer 77
3 Application of Optimization Methods to the Stability Analysis of Difference Schemes 161
4 Stability Analysis of Difference Schemes by Catastrophe Theory Methods 199
5 Construction of Multiply Connected Stability Regions of Difference Schemes by Computer Algebra and Pattern Recognition 240
6 Maximally Stable Difference Schemes 299
7 Stability Analysis of Nonlinear Difference Schemes 347
8 Symbolic Computation of Differential Approximations 403
Appendix A. Gas-Dynamic Matrices 446
Appendix B. REDUCE Program for Scheme (4.6.19) 451
Index 453
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