Singular Perturbation Techniques: A Comparison of the Method of Matched Asymptotic Expansions with That of Multiple Scales

A comparison is made between the uniformly valid asymptotic representations which can be developed for the solution of a singular perturbation boundary value problem involving a linear second order differential equation by using both the technique of matched asymptotic expansions and the method of m...

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Bibliographic Details
Published in:SIAM review 1977-07, Vol.19 (3), p.502-516
Main Author: Wollkind, David J.
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Boundary conditions
Boundary layers
Boundary value problems
Constant coefficients
High temperature
Investigations
Low temperature
Mathematical independent variables
Parameter identification
Partial differential equations
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Summary:A comparison is made between the uniformly valid asymptotic representations which can be developed for the solution of a singular perturbation boundary value problem involving a linear second order differential equation by using both the technique of matched asymptotic expansions and the method of multiple scales. Next, there is a discussion of some of the subtle features as well as the relative advantages, limitations, logical extensions, and typical applications of these two methods of obtaining uniformly valid asymptotic representations when applied to slightly more general singular perturbation problems which arise from investigations of various phenomena in the natural sciences. Finally, a parameter identification example relevant to biological population dynamics is presented to illustrate the fact that the mere knowledge of these singular perturbation techniques can be a powerful analytical tool.
ISSN:0036-1445
1095-7200
DOI:10.1137/1019072