Application of Chebyshev Polynomials to the Approximate Solution of Singular Integral Equations of the First Kind with Cauchy Kernel on the Real Half-line

被引：0

作者：

Shali, J. Ahmadi ^{[1
]}

Akbarfam, A. Jodayree ^{[1
]}

Kashfi, M. ^{[2
]}

机构：

[1] Univ Tabriz, Dept Math & Comp Sci, Tabriz, Iran

[2] Islamic Azad Univ, Dept Math, Shabestar Branch, Shabestar, Iran

来源：

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS | 2013年 / 4卷 / 01期

关键词：

Singular integral equation; Cauchy kernel; Approximate solution; Chebyshev polynomials; Collocation points;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, exact solution of the characteristic equation with Cauchy kernel on the real half-line is presented. Next, the Chebyshev polynomials of the second kind, U-n(x), and fourth kind, W-n(x), are used to derive numerical solutions of Cauchy-type singular integral equations of the first kind on the real half-line. The collocation points are chosen as the zeros of the Chebyshev polynomials of the first kind, Tn+2(x), and third kind, Vn+1(x). Moreover, estimations of errors of the approximated solutions are presented. The numerical results are given to show the accuracy of the methods presented.

引用

页码：21 / 28

页数：8

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