A Reliable Analytical Method for Solving Higher-Order Initial Value Problems. (2nd December 2013)

• Record Type: Journal Article
• Authors: Abu Arqub, Omar; Abo-Hammour, Zaer; Al-Badarneh, Ramzi; Momani, Shaher
• Other Names: Kilic Recai Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-12-02
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/673829
• Languages: English
• ISSNs: 1026-0226

Abstract

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.