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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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IMPACT FACTOR 2017: 0.755
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Volume 13, Issue 1


Volume 13 (2015)

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

Esmail Babolian
  • Department of Mathematics, Sciences And Research Branch, Islamic Azad University, Tehran, Iran
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Danial Hamedzadeh / Hossein Jafari / Asghar Arzhang Hajikandi
  • Department of Mathematics, Sciences And Research Branch, Islamic Azad University, Tehran, Iran
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Dumitru Baleanu
  • Department of Mathematics and Computer Sciences, Faculty of Art and Science, Balgat 06530, Ankara, Turkey
  • Institute of Space Sciences, Magurele-Bucharest, Romania
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-11-10 | DOI: https://doi.org/10.1515/phys-2015-0037


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.

Keywords: weakly singular; Fredholm integral equations; Taylor series; Galerkin method; Legendre functions


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About the article

Received: 2015-08-11

Accepted: 2015-09-16

Published Online: 2015-11-10

Citation Information: Open Physics, Volume 13, Issue 1, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2015-0037.

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©2015 E. Babolian et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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