Finite Difference Methods for Ordinary and Partial Differential Equations

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Finite Difference Methods for Ordinary and Partial Differential Equations
ISBN: 0898716292

Finite Difference Methods for Ordinary and Partial Differential Equations



Finite Difference Methods for Ordinary and Partial Differential Equations Society for Industrial and Applied Mathematics | July 10, 2007 | ISBN-10: 0898716292 | 357 pages | PDF | 14 Mb
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. The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations.

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