Differential Equations and Nonlinear Mechanics 
Volume 2008 (2008), Article ID 816787, 14 pages
doi:10.1155/2008/816787
Research Article

Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method

A. Sami Bataineh, M. S. M. Noorani, and I. Hashim

 School of Mathematical Sciences, Faculty of Science and Tecnology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Received 9 May 2008; Accepted 2 July 2008

Recommended by Yong Zhou

Abstract

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.