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9780898716399 Academic Inspection Copy

Finite Difference Schemes and Partial Differential Equations

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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.
John Strikwerda is Professor in the Department of Computer Sciences at the University of Wisconsin, Madison.
Preface to the Second Edition Preface to the First Edition Chapter 1: Hyperbolic Partial Differential Equations Chapter 2: Analysis of Finite Difference Schemes Chapter 3: Order of Accuracy of Finite Difference Schemes Chapter 4: Stability for Multistep Schemes Chapter 5: Dissipation and Dispersion Chapter 6: Parabolic Partial Differential Equations Chapter 7: Systems of Partial Differential Equations in Higher Dimensions Chapter 8: Second-Order Equations Chapter 9: Analysis of Well-Posed and Stable Problems Chapter 10: Convergence Estimates for Initial Value Problems Chapter 11: Well-Posed and Stable Initial-Boundary Value Problems Chapter 12: Elliptic Partial Differential Equations and Difference Schemes Chapter 13: Linear Iterative Methods Chapter 14: The Method of Steepest Descent and the Conjugate Gradient Method Appendix A: Matrix and Vector Analysis Appendix B: A Survey of Real Analysis Appendix C: A Survey of Results from Complex Anaylsis References Index.
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