Numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation
type: Item
instance of: scholarly article
title: Numerical solution of integral equations by means of the sinc collocation method based on the double exponential transformation
zbMATH Open document ID: 1072.65168
author: Mayinur Muhammad
author: Ahniyaz Nurmuhammad
author: Masatake Mori
author: Masaaki Sugihara
published in: Journal of Computational and Applied Mathematics
publication date: 2005-05-04T00:00:00Z
review text: Numerical solutions of linear Volterra integral equations of the first and second kind and Fredholm integral equations of the second kind are obtained by means of the sinc collocation method based on the double exponential transformation. A formula for numerical indefinite integration, developed earlier by \textit{M. Muhammad} and \textit{M. Mori} [ibid. 161, No.~2, 431--448 (2003; Zbl 1038.65018)], is applied to the Volterra integral equations. On the other hand, the conventional double exponential transformation for definite integrals is employed to the Fredholm integral equations. An error analysis of the method is given and in each case a convergence rate of \(O(\exp(-cN/\log N))\) for the error is established, where \(N\) is a parameter representing the number of terms of the sinc expansion. Numerical examples are given to show the above mentioned convergence rate and to confirm the high efficiency of the present method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 2164833
zbMATH Keywords: double exponential transformation
zbMATH Keywords: linear Volterra integral equations
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: sinc collocation method
zbMATH Keywords: numerical indefinite integration
zbMATH Keywords: error analysis
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.019
OpenAlex ID: W2050133252
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DOI: 10.1016/J.CAM.2004.09.019
description: scientific article; zbMATH DE number 2164833