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June 2008 Numerical Solution of Volterra Integral Equations with Weakly Singular Kernel Based on the DE-Sinc Method
Masatake Mori, Ahniyaz Nurmuhammad, Takefumi Murai
Japan J. Indust. Appl. Math. 25(2): 165-183 (June 2008).

Abstract

A method for numerical solution of Volterra integral equations of the second kind with a weakly singular kernel based on the double exponential (DE) transformation is proposed. In this method we first express the approximate solution in the form of a Sinc expansion based on the double exponential transformation by Takahasi and Mori in 1974 followed by collocation at the Sinc points. We also apply the DE formula to the kernel integration. In every sample equation a numerical solution with very high accuracy is obtained and a nearly exponential convergence rate $\exp(-cM/{\log M})$, $c>0$ in the error is observed where $M$ is a parameter representing the number of terms in the Sinc expansion. We compared the result with the one based on the single exponential (SE) transformation by Riley in 1992 which made us confirm the high efficiency of the present method.

Citation

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Masatake Mori. Ahniyaz Nurmuhammad. Takefumi Murai. "Numerical Solution of Volterra Integral Equations with Weakly Singular Kernel Based on the DE-Sinc Method." Japan J. Indust. Appl. Math. 25 (2) 165 - 183, June 2008.

Information

Published: June 2008
First available in Project Euclid: 3 July 2008

zbMATH: 1152.65121
MathSciNet: MR2431678

Rights: Copyright © 2008 The Japan Society for Industrial and Applied Mathematics

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Vol.25 • No. 2 • June 2008
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