Finite Difference Methods for Ordinary and Partial Differential Equations : Steady-State and Time-Dependent Problems

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  • Format: Paperback
  • Copyright: 7/10/2007
  • Publisher: Society for Industrial & Applied
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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

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
Table of Contents provided by Publisher. All Rights Reserved.

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