Nonlinear oscillators with rational terms: A new semi-analytical technique

This paper presents a new generalization of the standard homotopy analysis approach towards solving nonlinear oscillators equations with rational terms. By using this method, analytical approximations to the frequency of these oscillators and periodic solutions are calculated. Excellent agreement of the approximate frequencies and periodic solutions with exact ones is demonstrated and discussed. It is shown that this method is very simple, eective and convenient for solving nonlinear oscillator problems with rational terms.