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2015 | 13 | 1 |
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca

Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-08-11
zaakceptowano
2015-09-16
online
2015-11-10
Twórcy
  • Department of
    Mathematics, Sciences And Research Branch, Islamic Azad University,
    Tehran, Iran
  • Department of Mathematical Sciences, University of
    South Africa, UNISA 0003, South Africa
  • Department of Mathematics, University of Mazandaran,
    Babolsar, Iran
  • Department of
    Mathematics, Sciences And Research Branch, Islamic Azad University,
    Tehran, Iran
  • Department of Mathematics and Computer Sciences,
    Faculty of Art and Science, Balgat 06530, Ankara, Turkey
  • Institute of Space Sciences, Magurele-Bucharest,
    Romania
Bibliografia
  • [1] Y. Ren, B. Zhang, H. Qiao, J. Comput. Appl. Math. 110, 15 (1999)
  • [2] C. Schneider, Integr. Equat. Oper. Th. 2, 62 (1979)[Crossref]
  • [3] C. Schneider, Math. Comp. 36, 207 (1981)
  • [4] S. Xu, X. Ling,C. Cattani, G.N. Xie, X.J. Yang, Y. Zhao, Math.Probl. Eng. 2014, 914725 (2014)
  • [5] A.A. Badr, J. Comput. Appl. Math. 134, 191 (2001)
  • [6] R. Estrada, Ram P. Kanwal, Singular Integral Equations(Birkhauser, Boston, 2000)
  • [7] F.G. Tricomi, Integral Equations (Dover, New York, 1985)
  • [8] N.I. Muskhelishvili, Singular Integral Equations, 2nd edition (P.Noordhoff, N.V. Groningen, Holland, 1953)
  • [9] E. Babolian, A. Arzhang Hajikandi, J. Comput. Appl. Math. 235,1148 (2011)
  • [10] M. Lakestani, B. Nemati Saray, M. Dehghan, J. Comput. Appl.Math. 235, 3291 (2011)
  • [11] W. Jiang, M. Cui, Appl. Math. Comp. 202, 666 (2008)
  • [12] A. Pedas, E. Tamme, Appl. Numeric. Math. 61, 738 (2011)
  • [13] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions(Dover, New York, 1972)
  • [14] M. Abramowitz, I.A. Stegun, Pocketbook of Mathematical Functions(Verlag Harri Deutsch, Germany, 1984)
  • [15] G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists,5th edition (Academic Press, New York, 2001)
  • [16] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products,7th edition (Academic Press, Oxford, 2007)
  • [17] Philip J. Davis, Interpolation and Approximation (Dover Publications,New York, 1975)
  • [18] C. Allouch, P. Sablonnière, D. Sbibih, M. Tahrichi, J. Comput.Appl. Math. 233, 2855 (2010)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0037
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