Finite difference methods for ordinary and partial differential equations : steady-state and time-dependent problems / Randall J. LeVeque.

Format:

Book

Author/Creator:

LeVeque, Randall J., 1955-

Contributor:

Society for Industrial and Applied Mathematics.

Language:

English

Subjects (All):

Finite differences.

Differential equations.

Physical Description:

1 electronic text (xv, 341 p.) : ill., digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2007.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

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.

Contents:

I. Boundary Value Problems and Iterative Methods

1. Finite difference approximations

2. Steady states and boundary value problems

3. Elliptic equations

4. Iterative methods for sparse linear systems

II. Initial Value Problems

5. The initial value problem for ordinary differential equations

6. Zero-stability and convergence for initial value problems

7. Absolute stability for ordinary differential equations

8. Stiff ordinary differential equations

9. Diffusion equations and parabolic problems

10. Addiction equations and hyperbolic systems

11. Mixed equations

Appendixes: A. Measuring errors

B. Polynomial interpolation and orthogonal polynomials

C. Eigenvalues and inner-product norms

D. Matrix powers and exponentials

E. Partial differential equations

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 329-335) and index.

Title from title screen, viewed 10/20/2010.

Description based on title page of print version.

ISBN:

0-89871-783-3

Publisher Number:

OT98 siam

OT98 SIAM