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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 673829, 12 pages
http://dx.doi.org/10.1155/2013/673829
Research Article

A Reliable Analytical Method for Solving Higher-Order Initial Value Problems

1Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan
2Department of Mechatronics Engineering, Faculty of Engineering, University of Jordan, Amman 11942, Jordan
3Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13115, Jordan
4Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan

Received 2 July 2013; Accepted 23 September 2013

Academic Editor: Recai Kilic

Copyright © 2013 Omar Abu Arqub 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

In this article, a new analytical method has been devised to solve higher-order initial value problems for ordinary differential equations. This method was implemented to construct a series solution for higher-order initial value problems in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed method is based on the Taylor series expansion which constructs an analytical solution in the form of a polynomial and reproduces the exact solution when the solution is polynomial. This technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.