Singular-Perturbation Theory An Introduction with Applications Do… 9780521300421
Singular-Perturbation TheoryAn Introduction with Applications\nAuthor(s): Donald R. Smith\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521300421, 978-0521300421\nSynopsis\nThis 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,.
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