A higher order uniform convergence result for a turning point problem
type: Item
instance of: scholarly article
title: A higher order uniform convergence result for a turning point problem
zbMATH Open document ID: 0796.34039
DOI: 10.4171/ZAA/534
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1994-10-05T00:00:00Z
review text: Turning point problems of the form \(-\varepsilon u''- xa(x) u'+ b(x)u= f(x)\) with boundary conditions \(u(-1)= u(1)= 0\) are considered. Replacing the functions \(a(x)\), \(b(x)\) and \(f(x)\) by piecewise polynomials of degree \(k\), an iterative process is proposed which yields a \(k\)th order approximation to the solution, uniformly in \(\varepsilon> 0\). For the convergence proof a new stability estimate is developed.
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65J99
zbMATH DE Number: 509983
zbMATH Keywords: turning point problems
zbMATH Keywords: iterative process
zbMATH Keywords: approximation
zbMATH Keywords: convergence
zbMATH Keywords: stability estimate
author: Hans-G. Roos
author: Relja Vulanović
reviewed by: Ernst Hairer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/534
OpenAlex ID: W2561631324
description: scientific article; zbMATH DE number 509983