Analytical approximations for a conservative nonlinear singular oscillator in plasma physics

Mirzabeigy, A.; Kalami-Yazdi, M.; Yildirim, A.

doi:org/10.1016/j.joems.2012.05.001

Analytical approximations for a conservative nonlinear singular oscillator in plasma physics

Authors

¹ School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran 15914, Iran

² School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran

³ Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA Department of Mathematics, Ege University, Bornova-Izmir 35100, Turkey

org/10.1016/j.joems.2012.05.001

Abstract

A modified variational approach and the coupled homotopy perturbation method with
variational formulation are exerted to obtain periodic solutions of a conservative nonlinear singular
oscillator in plasma physics. The frequency–amplitude relations for the oscillator which the restoring force is inversely proportional to the dependent variable are achieved analytically. The approximate frequency obtained using the coupled method is more accurate than the modified variational approach and ones obtained using other approximate methods and the discrepancy between the approximate frequency using this coupled method and the exact one is lower than 0.31% for the whole range of values of oscillation amplitude. The coupled method provides a very good accuracy and is a promising technique to a lot of practical engineering and physical problems.

Keywords