The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators. (English) Zbl 1183.65083

Guo, Zhongjin; Leung, A. Y. T.

Appl. Math. Comput. 215, No. 9, 3163-3169 (2010).

Summary: 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 the proposed method. The results show that 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 the exact ones is demonstrated and discussed. The proposed method is very simple in its principle and has a great potential to be applied to other nonlinear oscillators.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

iterative homotopy harmonic balance method; parameter-expansion technique; conservative Helmholtz-Duffing oscillators; asymmetric equation; numerical examples; periodic solutions

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