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Reseach Article

Numerical Solution of Fourth Order Integro-differential Boundary Value Problems by Optimal Homotopy Asymptotic Method

by M. Khalid, Mariam Sultana, Faheem Zaidi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 106 - Number 2
Year of Publication: 2014
Authors: M. Khalid, Mariam Sultana, Faheem Zaidi
10.5120/18495-9557

M. Khalid, Mariam Sultana, Faheem Zaidi . Numerical Solution of Fourth Order Integro-differential Boundary Value Problems by Optimal Homotopy Asymptotic Method. International Journal of Computer Applications. 106, 2 ( November 2014), 38-44. DOI=10.5120/18495-9557

@article{ 10.5120/18495-9557,
author = { M. Khalid, Mariam Sultana, Faheem Zaidi },
title = { Numerical Solution of Fourth Order Integro-differential Boundary Value Problems by Optimal Homotopy Asymptotic Method },
journal = { International Journal of Computer Applications },
issue_date = { November 2014 },
volume = { 106 },
number = { 2 },
month = { November },
year = { 2014 },
issn = { 0975-8887 },
pages = { 38-44 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume106/number2/18495-9557/ },
doi = { 10.5120/18495-9557 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:38:21.439218+05:30
%A M. Khalid
%A Mariam Sultana
%A Faheem Zaidi
%T Numerical Solution of Fourth Order Integro-differential Boundary Value Problems by Optimal Homotopy Asymptotic Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 106
%N 2
%P 38-44
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for solving fourth order integro-differential equations.

References
  1. Agarwal, R. P. 1983 Boundary value problems for higher order integro-differential equations, Nonlinear Analysis: Theory, Methods & Applications, 259–270.
  2. Babolian, E. , Fattahzadeh, F. and Raboky, E. G. 2007. A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type, Applied Mathematics and Computation, 641–646.
  3. Borzabadi, A. H. , Kamyad, A. V. and Mehne, H. H. 2006. A different approach for solving the nonlinear Fredholm integral equations of the second kind, Applied Mathematics and Computation, 724–735.
  4. Avudainayagam, A. and Vani,C. 2000. Wavelet-Galerkin method for integro-di?erential equations, Applied Numerical Mathematics, 247-254.
  5. Rashed, M. T. 2004. Lagrange interpolation to compute the numerical solutions of di?erential, integral and integro-di?erential equations, Applied Mathematics and Computation, 869-878.
  6. Khader, M. M. 2012. Introducing an efficient modification of the variational iteration method by using Chebyshev polynomials, Applications and Applied Mathematics, 283–299.
  7. Sweilam, N. H. 2007. Fourth order integro-differential equations using variational iteration method, Computers & Mathematics with Applications, 1086–1091.
  8. Khader, M. M. 2012. Introducing an efficient modification of the homotopy perturbation method by using Chebyshev polynomials, Arab Journal of Mathematical Sciences, 61–71
  9. Sweilam, N. H. , Khader, M. M. and Al-Bar, R. F. 2008. Homotopy perturbation method for linear and nonlinear system of fractional integro-differential equations, International Journal of Computational Mathematics and Numerical Simulation, 73–87.
  10. Hosseini, S. M. and Shahmorad, S. 2003 Tau numerical solution of Fredholm integro-di?erential equations with arbitrary polynomial bases, Applied Mathematical Modeling, 145-154.
  11. Hashim, I. 2006. Adomian decomposition method for solving BVPs for fourth order integro-differential equations Journal of Computational and Applied Mathematics, 658-664.
  12. Wazwaz, A. M. 2001. A reliable algorithm for solving boundary value problems for higher-order integro-di?erential equations, Applied Mathematics and Computation,327-342.
  13. Maleknejad, K. and Mahmoudi, Y. 2003. Taylor polynomial solution of high-order nonlinear Volterra Fredholm integro-di?erential equations, Applied Mathematics and Computation, 641-653.
  14. Khader, M. M. and Mohamed, S. T. 2012. Numerical treatment for first order neutral delay differential equations using spline functions, Engineering Mathematics Letters, 32–43.
  15. Mohamed, S. T. and Khader, M. M. 2011. Numerical differential equations using the spline functions expansion, Global Journal of Pure and Applied Mathematics, 21–29. solutions to the second order Fredholm integro-
  16. Khader, M. M. and Hendy, A. S. 2012. The approximate and exact solutions of the fractional-order delay differential equations using Legendre pseudo-spectral method, International Journal of Pure and Applied Mathematics, 287–297.
  17. Khader, M. M. , Sweilam, N. H. and Mahdy, A. M. S. 2011. An efficient numerical method for solving the fractional difusion equation, Journal of Applied Mathematics and Bioinformatics, 1–12.
  18. Sweilam, N. H. , Khader, M. M. and Kota, W. Y. 2012. On the numerical solution of Hammerstein integral equations using Legendre approximation, International Journal of Applied Mathematical Research, 65–76.
  19. Yousefi, S. and Razzaghi, M. 2005. Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations, Mathematics and Computers in Simulation, 1–8.
  20. Marinca, V. and Herisanu, N. 2008. Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer, I. Comm. Heat Mass Transfer, 610-715
  21. Lakestani, M. and Dehghan, M. 2010. Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions, International Journal of Computer Mathematics, 1389–1394.
  22. Sweilam, N. H. , Khader, M. M. and Kota, W. Y. 2013. Numerical and Analytical Study for Fourth-Order-Integro-Differential Equations Using a Pseudospectral Method, Mathematical Problems in Engineering, Article ID 434753.
  23. Y?ld?r?m, A. 2008. Solution of BVPs for Fourth order integro-differential equations by using homotopy perturbation method, Computers & Mathematics with Applications, 3175-3180.
  24. Zhuang, Q. and Ren, Q. 2014. Numerical approximation of a nonlinearfourth order integro-differential equations by spectral method, Applied Mathematics and Computation, 775-783.
  25. Yang, L. and Cui, M. 2006. New algorithm for a class of nonlinear integro-di?erential equations in the reproducing kernel space, Appl. Math. Com-put. ,942-960
Index Terms

Computer Science
Information Sciences

Keywords

Fourth Order Integro-differential Equations Boundary Value problem Optimal Homotopy Asymptotic Method.