Singular-Perturbation Theory

Name: Singular-Perturbation Theory
Brand: Cambridge University Press
SKU: 9780521300421
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An Introduction with Applications

Autor: Donald R. Smith

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Editura: Cambridge University Press

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This book presents an introduction to singular-perturbation problems, problems which depend on a par...

Informații despre carte

Autor

Donald R. Smith

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

1985

Pagini

520

EAN

9780521300421

ISBN

0521300428

Enbook ID

02027188

Editura

Cambridge University Press

Greutate

800

Dimensiuni

158 x 235 x 37

Descriere completă

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.

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Singular-Perturbation Theory

An Introduction with Applications

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Descriere completă

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