Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 724927, 19 pages
doi:10.1155/2011/724927
Research Article

On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

Department of Mathematics, University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Received 8 November 2010; Accepted 7 February 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Che Haziqah Che Hussin and Adem Kiliçman. 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

We study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend and prove a theorem for nonlinear differential equations by using the DTM. The numerical examples show that the DTM is a good method compared to the ADM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to ADM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.