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