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

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 comput...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2013-01, Vol.2013 (2013), p.474-485-155
Main Authors: Abu Arqub, Omar, Abo-Hammour, Zaer, Al-Badarneh, Ramzi, Momani, Shaher
Format: Article
Language:English
Subjects:
Boundary value problems
Construction
Convergence (Mathematics)
Mathematical research
Series, Taylor's
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2013/673829