International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

Improvement of the homotopy perturbation method to nonlinear problems

J. F. Alzaidi
  • J. F. Alzaidi
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
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A. A. Alderremy
  • A. A. Alderremy
  • Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia.
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  •  Received: 15 November 2017
  •  Accepted: 31 January 2018
  •  Published: 28 February 2018

Abstract

This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations.

Key words: Homotopy perturbation method (HPM), shifted Jacobi polynomials, nonlinear ordinary differential equations.