Stabilitätskriterien für Näherungsverfahren bei singulären Integralgleichungen in \(L^ p\)
type: Item
instance of: scholarly article
title: Stabilitätskriterien für Näherungsverfahren bei singulären Integralgleichungen in \(L^ p\)
zbMATH Open document ID: 0659.65142
DOI: 10.4171/ZAA/271
author: Siegfried Prössdorf
author: Andreas Rathsfeld
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: Collocation and Galerkin methods are considered for the numerical solution of a class of singular integral equations. The operator is the sum of a multiplication operator and the product of a multiplication operator and a singular integral operator defined in terms of a Cauchy principal value defined on closed curves with a Lipschitz continuous tangential direction. The principal issue is the stability, i.e. the uniform invertibility of the matrices resulting from the use of the collocation or Galerkin procedure. In this paper, the authors establish a variety of stability results in \(L^ p\) spaces for \(1<p<\infty\). The principal tool is a representation of the discrete operators as sums of products of diagonal and circulant matrices.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 4078741
zbMATH Keywords: Collocation
zbMATH Keywords: Galerkin methods
zbMATH Keywords: singular integral equations
zbMATH Keywords: stability
reviewed by: Olof B. Widlund
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/271
OpenAlex ID: W2565065712
description: scientific article; zbMATH DE number 4078741