Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 842094, 15 pages
doi:10.1155/2009/842094
Research Article

Direct Solution of nth-Order IVPs by Homotopy Analysis Method

A. Sami Bataineh,1 M. S. M. Noorani,2 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

Received 3 February 2009; Accepted 4 June 2009

Academic Editor: Tasawar Hayat

Copyright © 2009 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

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).