Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

1 Issue per year


IMPACT FACTOR 2017: 0.755
5-year IMPACT FACTOR: 0.820

CiteScore 2017: 0.83

SCImago Journal Rank (SJR) 2017: 0.241
Source Normalized Impact per Paper (SNIP) 2017: 0.537

Open Access
Online
ISSN
2391-5471
See all formats and pricing
More options …
Volume 13, Issue 1

Issues

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

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.

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

References

  • [1] Y. Ren, B. Zhang, H. Qiao, J. Comput. Appl. Math. 110, 15 (1999) Google Scholar

  • [2] C. Schneider, Integr. Equat. Oper. Th. 2, 62 (1979) CrossrefGoogle Scholar

  • [3] C. Schneider, Math. Comp. 36, 207 (1981) Google Scholar

  • [4] S. Xu, X. Ling,C. Cattani, G.N. Xie, X.J. Yang, Y. Zhao, Math. Probl. Eng. 2014, 914725 (2014) Google Scholar

  • [5] A.A. Badr, J. Comput. Appl. Math. 134, 191 (2001) Google Scholar

  • [6] R. Estrada, Ram P. Kanwal, Singular Integral Equations (Birkhauser, Boston, 2000) Google Scholar

  • [7] F.G. Tricomi, Integral Equations (Dover, New York, 1985) Google Scholar

  • [8] N.I. Muskhelishvili, Singular Integral Equations, 2nd edition (P. Noordhoff, N.V. Groningen, Holland, 1953) Google Scholar

  • [9] E. Babolian, A. Arzhang Hajikandi, J. Comput. Appl. Math. 235, 1148 (2011) Google Scholar

  • [10] M. Lakestani, B. Nemati Saray, M. Dehghan, J. Comput. Appl. Math. 235, 3291 (2011) Google Scholar

  • [11] W. Jiang, M. Cui, Appl. Math. Comp. 202, 666 (2008) Google Scholar

  • [12] A. Pedas, E. Tamme, Appl. Numeric. Math. 61, 738 (2011) Google Scholar

  • [13] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972) Google Scholar

  • [14] M. Abramowitz, I.A. Stegun, Pocketbook of Mathematical Functions (Verlag Harri Deutsch, Germany, 1984) Google Scholar

  • [15] G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, 5th edition (Academic Press, New York, 2001) Google Scholar

  • [16] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, 7th edition (Academic Press, Oxford, 2007) Google Scholar

  • [17] Philip J. Davis, Interpolation and Approximation (Dover Publications, New York, 1975) Google Scholar

  • [18] C. Allouch, P. Sablonnière, D. Sbibih, M. Tahrichi, J. Comput. Appl. Math. 233, 2855 (2010) Google Scholar

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.

Export Citation

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

Comments (0)

Please log in or register to comment.
Log in