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

DOI10.1017/S0956792511000325zbMath1233.35011OpenAlexW2332818190MaRDI QIDQ3106306

Eleftherios Kirkinis, Robert E. jun. O'Malley

Publication date: 20 December 2011

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792511000325

zbMATH Keywords

perturbation theoryasymptotic methodsboundary layersmultiple scalesamplitude equation

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Asymptotic expansions of solutions to PDEs (35C20) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (3)

A general analytical approximation for nonlinear vibrations analysis of continuous systems using renormalization group method ⋮ A refined asymptotic perturbation method for nonlinear dynamical systems ⋮ Variation of Parameters and the Renormalization Group Method

Cites Work

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• Intermediate asymptotics and renormalization group theory
• The first boundary value problem for \(\epsilon\Delta u+A(x,y)u_x+B(x,y)u_y+C(x,y)u =D(x,y)\) for small \(\epsilon\)
• The Capriciousness of Numerical Methods for Singular Perturbations
• Asymptotic solutions of nonlinear second order differential equations with variable coefficients
• A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems
• Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
• An expansion method for singular perturbation problems

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