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
School of Mathematical Sciences, Faculty of Science and Tecnology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Received 9 May 2008; Accepted 2 July 2008
Academic Editor: Yong Zhou
Copyright © 2008 A. Sami Bataineh 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 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.