Singular Perturbation Theory
An Introduction with Applications
By (author) Donald R. Smith
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Singular Perturbation Theory by Donald R. Smith
Book DescriptionThis 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.
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Book DetailsISBN: 9780521300421
(228mm x 152mm x 33mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 30-Aug-1985
Country of Publication: United Kingdom
Books By Author Donald R. Smith
Singular-perturbation Theory, Paperback (March 2009)
This book presents an introduction to singular-perturbation problems.
Variational Methods in Optimization, Paperback (February 1999)» View all books by Donald R. Smith
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.
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