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A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Published online by Cambridge University Press:  12 August 2011

R. E. O'MALLEY Jr.  and
E. KIRKINIS
R. E. O'MALLEY Jr.
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, USA email: omalley@amath.washington.edu, kirkinis@amath.washington.edu
E. KIRKINIS
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420, USA email: omalley@amath.washington.edu, kirkinis@amath.washington.edu
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Abstract

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383–410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations.

Keywords

Asymptotic methodsPerturbation theoryBoundary layersMultiple scalesAmplitude equations

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 6 , December 2011 , pp. 613 - 629
Copyright
Copyright © Cambridge University Press 2011

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