A quadrature method for the Cauchy singular integral equations
type: Item
instance of: scholarly article
title: A quadrature method for the Cauchy singular integral equations
zbMATH Open document ID: 0856.65145
author: Youngmok Jeon
published in: Journal of Integral Equations and Applications
publication date: 1996-06-09T00:00:00Z
review text: The author considers a quadrature method for the Cauchy singular integral equation \[ au(t) + b\int^1_0 {u(s) \over s-t} ds=f(t), \quad t \in (0,1), \tag{1} \] with real constant coefficients \(a\) and \(b\). The method is based on the composite rectangular rule and on a mesh grading transformation, which yields fast convergence of the approximate solution by smoothing the singularities of the exact solution. A stability and convergence analysis is given by the use of local Mellin transformation techniques. The stability relies on a strong ellipticity result which, however, is stated as a conjecture and is only partially justified by numerical experiments. The paper presents numerical results, including the case of variable coefficients in equation (1).
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 885491
zbMATH Keywords: quadrature method
zbMATH Keywords: Cauchy singular integral equation
zbMATH Keywords: mesh grading transformation
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: local Mellin transformation techniques
zbMATH Keywords: numerical experiments
zbMATH Keywords: numerical results
reviewed by: Johannes Elschner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075897
OpenAlex ID: W2042234390
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DOI: 10.1216/JIEA/1181075897
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description: scientific article; zbMATH DE number 885491