African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 261

Review

Solving singular integral equations of the second kind using Chebyshev polynomials

Vivian Ndfutu Nfor
  • Vivian Ndfutu Nfor
  • Department of Fundamental Science, Higher Technical Teacher Training College, The University of Bamenda, Cameroon.
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Pascaline Liakem Ndukum
  • Pascaline Liakem Ndukum
  • Department of Computer Engineering, National Higher Polytechnic Institute, The University of Bamenda, Cameroon.
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  •  Received: 02 February 2023
  •  Accepted: 26 September 2023
  •  Published: 31 October 2023

Abstract

A numerical developed technique to solve Fredholm integral equation of the second kind with separable singular kernel is proposed. This technique relies on the truncated expansion functions of the kernels in the finite series of the weighted Chebyshev polynomials of first, second, third, and fourth kinds. Three numerical examples are presented for verification and validation of the developed technique. The results showed that even with small n, the numerical results are accurate.

Key words: Singular integral equations, singular kernel, Cauchy singularity, Chebyshev polynomial, weight function accuracy.