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Fluid DynamicsPart 2: Asymptotic Problems of Fluid Dynamics$
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Anatoly I. Ruban

Print publication date: 2015

Print ISBN-13: 9780199681747

Published to Oxford Scholarship Online: October 2015

DOI: 10.1093/acprof:oso/9780199681747.001.0001

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Perturbation Methods

Perturbation Methods

Chapter:
(p.4) 1 Perturbation Methods
Source:
Fluid Dynamics
Author(s):

Anatoly I. Ruban

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199681747.003.0002

Chapter 1 discusses the mathematical aspects of the asymptotic theory. It starts with basic definitions, using for this purpose the so-called coordinate asymptotic expansions. Then the chapter turns to asymptotic analysis of integrals and describe, among others, the method of steepest descent. However, the main attention is with parametric asymptotic expansions. These are used in a wide variety of fluid–dynamic problems, for which purpose a number of asymptotic techniques has been developed. We discuss in Chapter 1 the method of matched asymptotic expansions, the method of multiple scales, the method of strained coordinates, and the WKB method.

Keywords:   steepest descent method, matched asymptotic expansions, method of multiple scales

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