Analytical approximate solutions of the duffing-relativistic oscillator - Chowdhury, Md. Sazzad Hossien; Motakabber, S. M. A. (2015)

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The aim of this paper is to use high-order harmonic balance method (HBM) as a novel solution procedure for investigation of the Duffing-relativistic oscillation. Usually, a set of complex nonlinear algebraic equations is appeared when HBM is applied. Investigating analytically for such kind of complex nonlinear algebraic equations is tremendously difficult and cumbersome. In the present study, a small parameter is found, for which the power series solutions produces desired results. The obtained results are evaluated by comparing with the exact solutions computed numerically. The effect of initial conditions in the nonlinear natural frequencies is carried out and it is proved the proposed method is not only simple, but also more reliable for analysis for the Duffing-relativistic oscillator. The method is mainly illustrated in strongly nonlinear Duffing-relativistic oscillator, but it can be widely applicable in other problems arising nonlinear sciences and engineering.