Midpoint collocation for Cauchy singular integral equations
type: Item
instance of: scholarly article
title: Midpoint collocation for Cauchy singular integral equations
zbMATH Open document ID: 0762.65092
DOI: 10.1007/BF01396240
published in: Numerische Mathematik
publication date: 1993-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/133661
review text: The author studies the numerical solution of a Cauchy singular integral equation of the first kind on a smooth closed curve, using continuous piecewise linear functions and collocation at the midpoints of the underlying grid. He presents an interesting and new approach to the convergence analysis of this method, only assuming that the local mesh ratio is bounded. Suboptimal rates of convergence are proved using a discrete maximum principle for a modified form of the collocation equations. The results are extended to the case of piecewise constant midpoint collocation for the logarithmic potential operator.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 118309
zbMATH Keywords: suboptimal rates of convergence
zbMATH Keywords: Cauchy singular integral equation of the first kind
zbMATH Keywords: piecewise linear
zbMATH Keywords: midpoint collocation
zbMATH Keywords: logarithmic potential operator
author: Graeme Chandler
reviewed by: Johannes Elschner
MaRDI profile type: Publication
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OpenAlex ID: W2052865669
description: scientific article; zbMATH DE number 118309