A rectangular quadrature method for logarithmically singular integral equations of the first kind
type: Item
instance of: scholarly article
title: A rectangular quadrature method for logarithmically singular integral equations of the first kind
zbMATH Open document ID: 0764.65083
author: B. Bialecki
author: Yi Yan
published in: Journal of Integral Equations and Applications
publication date: 1993-01-26T00:00:00Z
review text: By extracting the logarithmic singularity, the given singular integral equation is first transformed into an equivalent integral equation whose integrand is regular and periodic. The problem is then discretized by using rectangular quadrature rules and collocation at the quadrature nodes. The authors present a detailed analysis of the discretization error and the stability of the method; it is also shown that Richardson extrapolation accelerates the convergence from \(O(h^ 3)\) to \(O(h^ 5)\). An analysis of the rectangular quadrature rule can also be found in a recent paper by \textit{J. Saranen} [J. Integral Equations Appl. 3, No. 4, 575-600 (1991; Zbl 0747.65100)]; the stability of collocation methods for first-kind integral equations with logarithmic singularity has been investigated using a similar approach by the second author [Math. Comput. 54, No. 189, 139-154 (1990; Zbl 0685.65121)] and by \textit{I. G. Graham} and the second author [J. Aust. Math. Soc., Ser. B 33, No. 1, 39-64 (1991; Zbl 0738.65097)].
reviewed by: H. Brunner
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 86117
zbMATH Keywords: error analysis
zbMATH Keywords: convergence acceleration
zbMATH Keywords: logarithmic singularity
zbMATH Keywords: collocation
zbMATH Keywords: stability
zbMATH Keywords: Richardson extrapolation
zbMATH Keywords: quadrature rule
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075696
OpenAlex ID: W2041942629
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DOI: 10.1216/JIEA/1181075696
description: scientific article; zbMATH DE number 86117