Journal of Applied Mathematics
Volume 2012 (2012), Article ID 581481, 13 pages
http://dx.doi.org/10.1155/2012/581481
Research Article

A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders

A. M. A. El-Sayed,1 A. Elsaid,2 and D. Hammad2

1Faculty of Science, Alexandria University, Alexandria, Egypt
2Mathematics & Engineering Physics Department, Faculty of Engineering, Mansoura University, P.O. Box 35516, Mansoura, Egypt

Received 16 October 2011; Accepted 8 December 2011

Academic Editor: Livija Cveticanin

Copyright © 2012 A. M. A. El-Sayed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The reliable treatment of homotopy perturbation method (HPM) is applied to solve the Klein-Gordon partial differential equation of arbitrary (fractional) orders. This algorithm overcomes the difficulty that arises in calculating complicated integrals when solving nonlinear equations. Some numerical examples are presented to illustrate the efficiency of this technique.