A modified discrete spectral collocation method for first kind integral equations with logarithmic kernel
type: Item
instance of: scholarly article
title: A modified discrete spectral collocation method for first kind integral equations with logarithmic kernel
zbMATH Open document ID: 0803.65136
published in: Journal of Integral Equations and Applications
publication date: 1995-01-02T00:00:00Z
review text: The author considers Symm's integral equation, i.e. a first kind integral equation with logarithmic kernel. He proposes a modification of the discrete Galerkin method presented by \textit{K. E. Atkinson} [ibid. 1, No. 3, 343-363 (1988; Zbl 0676.65140)]. This method has the computational complexity of the trigonometric collocation but it still retains the stability and the convergence properties of the original trigonometric Galerkin method. The given theory is illustrated by numerical experiments.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 575548
zbMATH Keywords: discrete spectral collocation method
zbMATH Keywords: Symm's integral equation
zbMATH Keywords: first kind integral equation with logarithmic kernel
zbMATH Keywords: discrete Galerkin method
zbMATH Keywords: computational complexity
zbMATH Keywords: trigonometric collocation
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
author: J. Saranen
reviewed by: Lechoslaw Hącia
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075777
OpenAlex ID: W1964275252
cites work: A discrete Galerkin method for first kind integral equations with a logarithmic kernel
cites work: The Numerical Solution of First-Kind Logarithmic-Kernel Integral Equations on Smooth Open Arcs
cites work: A Spectral Galerkin Method for a Boundary Integral Equation
cites work: Quadrature Methods for Strongly Elliptic Equations of Negative Order on Smooth Closed Curves
cites work: Quadrature methods for logarithmic-kernel integral equations on closed curves
cites work: Cosine Change of Variable for Symm's Integral Equation on Open Arcs
cites work: On integral equations of the first kind with logarithmic kernels
DOI: 10.1216/JIEA/1181075777
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description: scientific article; zbMATH DE number 575548