International Journal of Differential Equations
Volume 2009 (2009), Article ID 710250, 13 pages
doi:10.1155/2009/710250
Research Article

On a New Reliable Algorithm

A. K. Alomari,1 M. S. M. Noorani,2 and R. Nazar2

1Department of Science, Faculty of Nursing and Sciences, Jerash Private University, 26150 Jerash, Jordan
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

Received 8 August 2009; Revised 30 November 2009; Accepted 22 December 2009

Academic Editor: Dumitru Bǎleanu

Copyright © 2009 A. K. Alomari 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

An analytical expression for the solution of the prey-predator problem by an adaptation of the homotopy analysis method (HAM) is presented. The HAM is treated as an algorithm for approximating the solution of the problem in a sequence of time intervals; that is, HAM is converted into a hybrid numeric-analytic method called the multistage HAM (MSHAM). Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.