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Singular-Perturbation Theory
Donald R. Smith
其他書名
An Introduction with Applications
出版
Cambridge University Press
, 1985-08-30
主題
Mathematics / General
Mathematics / Calculus
Mathematics / Differential Equations / General
Mathematics / Functional Analysis
ISBN
0521300428
9780521300421
URL
http://books.google.com.hk/books?id=cEszbdam0zwC&hl=&source=gbs_api
EBook
SAMPLE
註釋
This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave non-uniformly as the parameter tends toward some limiting value of interest. The author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the linearization. This book will be useful to students at the graduate and senior undergraduate levels studying perturbation theory for differential equations, and to pure and applied mathematicians, engineers, and scientists who use differential equations in the modelling of natural phenomena.