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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 758195, 7 pages
Research Article

Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators

1Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
2Department of Science, Faculty of Science, Princess Sumaya University for Technology, Amman 11941, Jordan
3Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan

Received 26 March 2014; Revised 21 May 2014; Accepted 22 May 2014; Published 17 June 2014

Academic Editor: Shao-Ming Fei

Copyright © 2014 Banan Maayah 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.


A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.