Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems / Edition 1

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Overview

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.

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What People Are Saying

Peter Lax
"I heartily recommend this text to students who want a solid grounding in the theory and practice of solving differential equations-ordinary and partial. The book well repays serious study."--(Peter Lax, Professor, Courant Institute of Math)
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Product Details

  • ISBN-13: 9780898716290
  • Publisher: SIAM
  • Publication date: 7/10/2007
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 350
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.71 (d)

Meet the Author

Randall J. LeVeque is a Professor in the Departments of Mathematics and Applied Mathematics at the University of Washington, Seattle.

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Table of Contents

Preface; Part 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; Part 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. Advection equations and hyperbolic systems; 11. Mixed equations; 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.

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