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

Authors

  • J. Ahmadi Shali Department of Mathematics and Computer Science, University of Tabriz, Tabriz
  • A. Jodayree Akbarfam Department of Mathematics and Computer Science, University of Tabriz, Tabriz
  • M. Kashfi Department of Mathematics, Islamic Azad University, Shabestar Branch, Shabestar

DOI:

https://doi.org/10.26713/cma.v4i1.159

Keywords:

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

Abstract

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, $T_{n+2}(x)$, and third kind, $V_{n+1}(x)$. Moreover, estimations of errors of the approximated solutions are presented. The numerical results are given to show the accuracy of the methods presented.

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CITATION

How to Cite

Shali, J. A., Akbarfam, A. J., & Kashfi, M. (2013). Application of Chebyshev Polynomials to the Approximate Solution of Singular Integral Equations of the First Kind with Cauchy Kernel on the Real Half-line. Communications in Mathematics and Applications, 4(1), 21–28. https://doi.org/10.26713/cma.v4i1.159

Issue

Section

Research Article