Finite difference methods for ordinary and partial differential equations : steady-state and time-dependent problems

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Title:

Finite difference methods for ordinary and partial differential equations : steady-state and time-dependent problems

Author:

LeVeque, Randall J., 1955-

ISBN:

9780898716290

Personal Author:

LeVeque, Randall J., 1955-

Publication Information:

Philadelphia , PA : Society for Industrial and Applied Mathematics, c2007.

Physical Description:

xv, 341 p. : ill. ; 26 cm.

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 -- III. Appendices. App. A. Measuring errors -- App. B. Polynomial interpolation and orthogonal polynomials -- App. C. Eigenvalues and inner-product norms -- App. D. Matrix powers and exponentials -- App. E. Partial differential equations.

Abstract:

"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 POE 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." "This book is designed as an introductory graduate-level textbook on finite difference methods and their analysis. It is also appropriate for researchers who desire an introduction to the use of these methods."--BOOK JACKET.

Subject Term:

Finite differences.

Differential equations.

Electronic Access:

Table of contents only http://www.loc.gov/catdir/enhancements/fy0707/2007061732-t.html
Publisher description http://www.loc.gov/catdir/enhancements/fy0707/2007061732-d.html
Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0708/2007061732-b.html

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Library	Material Type	Item Barcode	Shelf Number	Copy	Status
Searching... 1:IIEMSA	1:GEN-BOOK	33168025793635	515.35 L657F 2007	1	Searching... Unknown

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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.