The iterative homotopy harmonic balance method for conservative Helmholtz–Duffing oscillators

Abstract

An approach that the iterative homotopy harmonic balance method which incorporates salient features of both the parameter-expansion and the harmonic balance is presented to solve conservative Helmholtz–Duffing oscillators. Since the behaviors of the solutions in the positive and negative directions are quite different, the asymmetric equation is separated into two auxiliary equations. The auxiliary equations are solved by proposed method. The results show it works very well for the whole range of initial amplitudes in a variety of cases, and the excellent agreement of the approximate periods and periodic solutions with exact ones have been demonstrated and discussed. And, the proposed method is very simple in its principle and has great potential to be applied to other nonlinear oscillators.