Japan Journal of Industrial and Applied Mathematics

Numerical Solution of Volterra Integral Equations with Weakly Singular Kernel Based on the DE-Sinc Method

Masatake Mori, Ahniyaz Nurmuhammad, and Takefumi Murai

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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.

Article information

Source
Japan J. Indust. Appl. Math., Volume 25, Number 2 (2008), 165-183.

Dates
First available in Project Euclid: 3 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1215118761

Mathematical Reviews number (MathSciNet)
MR2431678

Zentralblatt MATH identifier
1152.65121

Keywords
double exponential transformation DE transformation integral equation Sinc method weakly singular kernel

Citation

Mori, Masatake; Nurmuhammad, Ahniyaz; Murai, Takefumi. Numerical Solution of Volterra Integral Equations with Weakly Singular Kernel Based on the DE-Sinc Method. Japan J. Indust. Appl. Math. 25 (2008), no. 2, 165--183. https://projecteuclid.org/euclid.jjiam/1215118761


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