Collocation methods for second kind integral equations with non-compact operators
type: Item
instance of: scholarly article
title: Collocation methods for second kind integral equations with non-compact operators
zbMATH Open document ID: 0703.65090
DOI: 10.1216/JIE-1989-2-1-1
author: Elsie Sterbin Gottlieb
published in: Journal of Integral Equations and Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors analyze the uniform convergence of collocation solutions in the space of piecewise continuous polynomial splines of degree r-1 for linear integral equations of the second kind on the half line, where the integral operator is a compact perturbation of a Wiener-Hopf operator. If the underlying mesh is suitably graded, i.e. if the mesh points \(\{s_ i:\) \(i=1,...,n\}\) are given by \(s_ i=(r/\mu)\cdot \ell n(m/(m+1-i))\) (for appropriately chosen \(m\geq n\), and with the real number \(\mu >0\) characterizing the exponential decay of the exact solution at infinity), then optimal order of convergence holds for the collocation solution. Optimal superconvergence results for the corresponding iterated collocation solution are established on analogously graded meshes. These convergence results are then extended to boundary integral equations on polygonal domains. The paper generalizes and complements a number of results contained by the second author and \textit{A. Spence} [IMA J. Numer. Anal. 6, 153-172 (1986; Zbl 0593.65095)] and by \textit{G. A. Chandler} and \textit{I. G. Graham} [Math. Comp. 50, 125-138 (1988; Zbl 0639.65074)].
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4153847
zbMATH Keywords: uniform convergence
zbMATH Keywords: collocation
zbMATH Keywords: polynomial splines
zbMATH Keywords: linear integral equations of the second kind on the half line
zbMATH Keywords: Wiener-Hopf operator
zbMATH Keywords: optimal order of convergence
zbMATH Keywords: superconvergence
zbMATH Keywords: boundary integral equations
reviewed by: H. Brunner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4153847