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

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SIAM, Sep 6, 2007 - Mathematics - 339 pages
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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.
 

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Contents

OT98_ch1
3
OT98_ch2
13
OT98_ch3
59
OT98_ch4
69
OT98_ch5
113
OT98_ch6
137
OT98_ch7
149
OT98_ch8
167
OT98_ch10
201
OT98_ch11
233
OT98_appa
245
OT98_appb
259
OT98_appc
269
OT98_appd
285
OT98_appe
311
OT98_bm
329

OT98_ch9
181

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About the author (2007)

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.

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