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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 513473, 11 pages
http://dx.doi.org/10.1155/2014/513473
Research Article

Approximate Periodic Solutions for Oscillatory Phenomena Modelled by Nonlinear Differential Equations

“Politehnica” University of Timişoara, Department of Mathematics, Piata Victoriei 2, 300006 Timişoara, Romania

Received 14 January 2014; Accepted 29 March 2014; Published 23 April 2014

Academic Editor: Baocang Ding

Copyright © 2014 Constantin Bota 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

We apply the Fourier-least squares method (FLSM) which allows us to find approximate periodic solutions for a very general class of nonlinear differential equations modelling oscillatory phenomena. We illustrate the accuracy of the method by using several significant examples of nonlinear problems including the cubic Duffing oscillator, the Van der Pol oscillator, and the Jerk equations. The results are compared to those obtained by other methods.