title: Fourier series expansion for nonlinear Hamiltonian oscillators.
abstract: 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.
authors.affiliation: Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Cerdanyola del Vallès), Spain.
authors.forename: Vicenç
authors.initials: V
authors.lastname: Méndez
authors.forename: Cristina
authors.initials: C
authors.lastname: Sans
authors.forename: Daniel
authors.initials: D
authors.lastname: Campos
authors.forename: Isaac
authors.initials: I
authors.lastname: Llopis