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.
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.
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|Item Type:||Journal Article|
|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|
|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|
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