The Numerical Solution of Ordinary and Partial Differential Equations

Granville Sewell

334 pages, parution le 17/08/2005 (2^eme édition)

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Résumé

Learn to write programs to solve ordinary and partial differential equations

The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations.

The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers.

The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems.

A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.

L'auteur - Granville Sewell

Granville Sewell, PHD, is Visiting Professor of Mathematics at Texas A&M University and Professor of Mathematics at the University of Texas at El Paso. He is the principal developer of PDE2D, a general-purpose partial differential equation solver. Dr. Sewell has written three books and published more than fifty articles on numerical methods and applications.

Sommaire

Preface
Direct Solution of Linear Systems
Initial Value Ordinary Differential Equations
The Initial Value Diffusion Problem
The Initial Value Transport and Wave Problems
Boundary Value Problems
The Finite Element Method
Appendix A: Solving PDEs with PDE2D
Appendix B: The Fourier Stability Method
Appendix C: MATLAB Programs
Appendix D: Can 'Anything' Happen in an Open System?
Appendix E: Answers to Selected Exercises
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Granville Sewell
Parution	17/08/2005
Édition	2^eme édition
Nb. de pages	334
Format	16 x 24,5
Couverture	Relié
Poids	618g
Intérieur	Noir et Blanc
EAN13	9780471735809
ISBN13	978-0-471-73580-9