Finite Difference Schemes and Partial Differential Equations
2nd Edition
Will be published approx. on 30. November 2007
Book
Paperback/Softback
447 pages
978-0-89871-639-9 (ISBN)
Description
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.
More details
Edition
Second Edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Edition type
New edition
Dimensions
Height: 255 mm
Width: 180 mm
Thickness: 24 mm
Weight
750 gr
ISBN-13
978-0-89871-639-9 (9780898716399)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
John Strikwerda is Professor in the Department of Computer Sciences at the University of Wisconsin, Madison.
Content
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.
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.