On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

Esmail Babolian 1 , Danial Hamedzadeh 2 , Hossein Jafari 3 , Asghar Arzhang Hajikandi 1 , and Dumitru Baleanu 4 , 5
  • 1 Department of Mathematics, Sciences And Research Branch, Islamic Azad University, Tehran, Iran
  • 2 Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa
  • 3 Department of Mathematics, University of Mazandaran, Babolsar, Iran
  • 4 Department of Mathematics and Computer Sciences, Faculty of Art and Science, Balgat 06530, Ankara, Turkey
  • 5 Institute of Space Sciences, Magurele-Bucharest, Romania

Abstract

This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x0, y0) is used. The integrals that appear in this method are computed exactly and some of these integrals are computed with the Cauchy principal value without using numerical quadratures. The solution in the Legendre polynomial form generates a system of linear algebraic equations, this system is solved numerically. Through numerical examples, performance of the present method is discussed concerning the accuracy of the method.

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