A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

O'Malley, R. E. & Kirkinis, E. (2011) A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems. European Journal of Applied Mathematics, 22(6), pp. 613-629.

View at publisher


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. © 2011 Cambridge University Press.

Impact and interest:

1 citations in Scopus
Search Google Scholar™
4 citations in Web of Science®

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 73425
Item Type: Journal Article
Refereed: Yes
Keywords: Amplitude equations, Asymptotic methods, Boundary layers, Multiple scales, Perturbation theory, Amplitude equation, Asymptotic method, Matched asymptotic expansion, Multiple scale, Multiscale method, Ordinary and partial differential equations, Renormalization, Scale method, Singular perturbation problems, Singularly perturbed, Singularly perturbed problem, Two time scale, Amplitude modulation, Asymptotic analysis, Ordinary differential equations, Partial differential equations, Statistical mechanics, Perturbation techniques
DOI: 10.1017/S0956792511000325
ISSN: 09567925 (ISSN)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 07 Jul 2014 22:31
Last Modified: 09 Jul 2014 05:49

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page