A modified Mickens iteration procedure for nonlinear oscillators

Based on the Mickens procedure, a new iteration scheme is proposed for nonlinear oscillators. Different from the existing Mickens procedures, in the proposed procedure, the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear. Taking the Duffing equation as an illustrative example, excellent approximations can be easily obtained. Furthermore, the proposed procedure is extended to obtain the limit cycle of the van der Pol equation. Additionally, a computational disadvantage of the Mickens procedure is eliminated.