On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind

Authors

  • Mohammad Abdulkawi Mahiub Department of Mathematics, Faculty of Science,University Putra Malaysia
  • Z. K. Eshkuvatov
  • N. M. A. Nik Long

Keywords:

Integral equations, Cauchy singular kernel, Chebyshev polynomials, Approximation

Abstract

This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x=-1, for Cauchy type singular integral equations of the first kind on the interval [-1,1]. The solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the third kind, and then computing the Cauchy singular integral which is obtained analytically. The known force function is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this approximate method is shown for characteristic equation when the force function is a cubic. The particular result also shows the exactness of this method.

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Published

2009-08-18

Issue

Vol. 2 No. 3: (July 2009)

Section

Nonlinear Analysis

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How to Cite

On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind. (2009). European Journal of Pure and Applied Mathematics, 2(3), 462-472. https://www.ejpam.com/index.php/ejpam/article/view/304