The approximate solution of a class of Fredholm integral equations with a weakly singular kernel

被引：7

作者：

Babolian, E. ^{[1
]}

Hajikandi, A. Arzhang ^{[1
]}

机构：

[1] Islamic Azad Univ, Sci & Res Branch, Dept Math, Tehran, Iran

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 05期

关键词：

Cauchy kernel; Weakly singular; Taylor series; Galerkin method; Legendre functions;

D O I：

10.1016/j.cam.2010.07.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A method for finding the numerical solution of a weakly singular Fredholm integral equation of the second kind is presented. The Taylor series is used to remove singularity and Legendre polynomials are used as a basis. Furthermore, the Legendre function of the second kind is used to remove singularity in the Cauchy type integral equation. The integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the Cauchy principal value sense without using numerical quadratures. Four examples are given to show the accuracy of the method. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1148 / 1159

页数：12

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