Journal of Applied Mathematics
Volume 2012 (2012), Article ID 906341, 11 pages
Research Article

An Optimal Iteration Method for Strongly Nonlinear Oscillators

1Department of Mechanics and Vibration, Politehnica University of Timisoara, Boulevard Mihai Viteazu, No. 1, 300222 Timisoara, Romania
2Department of Electromechanics and Vibration, Center for Advanced and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Boulevard Mihai Viteazu, No. 24, 300223 Timisoara, Romania

Received 5 July 2011; Revised 14 September 2011; Accepted 18 September 2011

Academic Editor: Xianhua Tang

Copyright © 2012 Vasile Marinca and Nicolae Herişanu. 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.


We introduce a new method, namely, the Optimal Iteration Perturbation Method (OIPM), to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solutions. The main advantage of this approach consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. A very good agreement was found between approximate and numerical solutions, which prove that OIPM is very efficient and accurate.