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.
Publié le : 2008-06-15
Classification:
double exponential transformation,
DE transformation,
integral equation,
Sinc method,
weakly singular kernel
@article{1215118761,
author = {Mori, Masatake and Nurmuhammad, Ahniyaz and Murai, Takefumi},
title = {Numerical Solution of Volterra Integral Equations with Weakly Singular Kernel Based on the DE-Sinc Method},
journal = {Japan J. Indust. Appl. Math.},
volume = {25},
number = {1},
year = {2008},
pages = { 165-183},
language = {en},
url = {http://dml.mathdoc.fr/item/1215118761}
}
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., Tome 25 (2008) no. 1, pp. 165-183. http://gdmltest.u-ga.fr/item/1215118761/