Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 842094, 15 pages
doi:10.1155/2009/842094
Direct Solution of nth-Order IVPs by Homotopy Analysis Method
A.Sami Bataineh1
, M.S.M. Noorani2
and I. Hashim2
1Department of Mathematics, Irbid National University, Irbid 2600, Jordan
2Centre for Modelling and Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia (National University of Malaysia), 43600 Bangi Selangor, Malaysia
Abstract
Direct solution of a class of nth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).