A reduction principle for singular perturbation problems
type: Item
instance of: scholarly article
title: A reduction principle for singular perturbation problems
zbMATH Open document ID: 0933.34061
DOI: 10.1016/S0096-3003(98)00042-3
author: K. Appert
published in: Applied Mathematics and Computation
publication date: 2000-03-19T00:00:00Z
review text: Consider singularly perturbed systems of the type \[ \begin{multlined} f(x^{(m)}, x^{(m-1)}, \dots ,x,y^{(n)}, y^{(n-1)}, \dots ,y)=0,\\ y^{(r)} + \varepsilon g(y^{(p)} ,\dots ,y,x^{(q)}, \dots ,x) + h(y^{(r-1)}, \dots ,y,x^{(s)} ,\dots ,x)=0,\end{multlined} \tag{*} \] with \(p >r, q>s\). The solution to \((*)\) satisfying initial or boundary conditions consists of a regular part (outer solution) and a boundary layer correction. The authors propose an algorithm to construct the outer solution to \((*)\) and apply it to some examples. There is no mathematical justification of this approach. The remarks of the authors concerning critical (degenerate) cases are given without any justifications. The references contain no recent result on singularly perturbed problems.
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 1311071
zbMATH Keywords: reduction principle
zbMATH Keywords: singular perturbation
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: s0096-3003(98)00042-3
OpenAlex ID: W2036302782
description: scientific article; zbMATH DE number 1311071