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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 135465, 10 pages
http://dx.doi.org/10.1155/2014/135465
Research Article

A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

1Applied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
2Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan

Received 12 September 2013; Accepted 11 February 2014; Published 25 March 2014

Academic Editor: Hak-Keung Lam

Copyright © 2014 Mohammed AL-Smadi 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

The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.