Fourier series expansion for nonlinear Hamiltonian oscillators

Vicenç Méndez, Cristina Sans, Daniel Campos, Isaac Llopis

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate. © 2010 The American Physical Society.
Original languageEnglish
Article number066201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Publication statusPublished - 1 Jun 2010

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