Optimal homotopy asymptotic approach to nonlinear oscillators with discontinuities

In this paper a version of the optimal homotopy asymptotic method (OHAM) has been proposed and applied to nonlinear oscillators with discontinuities. The main objective was to obtain highly accurate analytical solutions for a particular antisymmetric constant force oscillator using this new procedure. The proposed procedure proved to be very effective and accurate and did not require linearization or small parameters in the equation. It was found that OHAM works very well for whole range of initial amplitudes since an excellent agreement of the approximate frequencies and periodic solutions with the numerical ones has been demonstrated.