Finite Difference Methods for Ordinary and Partial Differential Equations

by Leveque, Randall J.

• ISBN13: 9780898716290
• ISBN10: 0898716292
• Format: Paperback
• Copyright: 2007-07-10
• Publisher: SIAM

Summary

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. Exercises and student projects are available on the book's webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.

Author Biography

About the Author Randall J. LeVeque is a Professor in the Department of Applied Mathematics at the University of Washington, Seattle. He is an editor of the Survey and Review section of SIAM Review.

Table of Contents

Preface

Boundary Value Problems and Iterative Methods

Finite difference approximations

Steady states and boundary value problems

Elliptic equations

Iterative methods for sparse linear systems

Initial Value Problems

The initial value problem for ordinary differential equations

Zero-stability and convergence for initial value problems

Absolute stability for ordinary differential equations

Stiff ordinary differential equations

Diffusion equations and parabolic problems

Advection equations and hyperbolic systems

Mixed equations

Measuring errors

Polynomial interpolation and orthogonal polynomials

Eigenvalues and inner-product norms

Matrix powers and exponentials

Partial differential equations

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.