Finite Difference Schemes and Partial Differential Equations
Finite Difference Schemes and Partial Differential Equations
This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes. This is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes. In this updated edition the notion of a stability domain is now included in the definition of stability and is more prevalent throughout the book. The author has also added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes.
- Provides an introduction that will enable students to progress to more advanced texts and to knowledgeably implement the basic methods
- Researchers in numerical analysis also will find it a useful reference for studying stability theory for finite difference schemes applied to linear partial differential equations
- The author has added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes
Product details
November 2004Hardback
9780898715675
450 pages
260 × 181 × 27 mm
1.005kg
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Table of Contents
- Preface to the second edition
- Preface to the first edition
- 1. Hyperbolic partial differential equations
- 2. Analysis of finite difference Schemes
- 3. Order of accuracy of finite difference schemes
- 4. Stability for multistep schemes
- 5. Dissipation and dispersion
- 6. Parabolic partial differential equations
- 7. Systems of partial differential equations in higher dimensions
- 8. Second-order equations
- 9. Analysis of well-posed and stable problems
- 10. Convergence estimates for initial value problems
- 11. Well-posed and stable initial-boundary value problems
- 12. Elliptic partial differential equations and difference schemes
- 13. Linear iterative methods
- 14. The method of steepest descent and the conjugate gradient method
- Appendix A. Matrix and vectoranalysis
- Appendix B. A survey of real analysis
- Appendix C. A Survey of results from complex analysis
- References
- Index.
