Application of He's homotopy perturbation method to the Duffing-harmonic oscillator

The homotopy perturbation method is used to solve the Duffing-harmonic oscillator. Only one iteration leads to high accuracy of the approximate solution, which is valid for the whole range of amplitudes, the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed.