A hybrid multiple scale procedure for boundary layers involving several dissimilar scales
type: Item
instance of: scholarly article
title: A hybrid multiple scale procedure for boundary layers involving several dissimilar scales
zbMATH Open document ID: 0924.76096
author: J. Majdalani
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1999-11-01T00:00:00Z
review text: Many boundary value problems involving rapidly decaying oscillations can be put into the form \(\varepsilon \frac {d^{2}f}{dx^2}+a(x)\frac{df}{dx}+b(x)f=0\), \(x \in{[0,1]}\), where \(0<\varepsilon \ll 1\), \(a(x)\) and \(b(x)\) are continuous functions of \(x\), and \(f\) varies rapidly in regions of \(x\). The aim of this article is to devise a method to solve such problems by using well-known perturbation methods which involve four widely varying scales for independent variables. The author suggests such a composite scale which can be reduced to the dissimilar scales in the corresponding intervals and leads to an accurate uniformly valid solution.
Mathematics Subject Classification ID: 76N20
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 1251166
zbMATH Keywords: rapidly decaying oscillations
zbMATH Keywords: perturbation methods
zbMATH Keywords: uniformly valid solution
zbMATH Keywords: asymptotic expansions
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: s000330050126
OpenAlex ID: W2129261357
DOI: 10.1007/S000330050126
description: scientific article; zbMATH DE number 1251166