Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

Abstract

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions.

Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity.

GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75 

DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504