Analytic Approach to Investigation of Fluctuation and Frequency of the Oscillators with Odd and Even Nonlinearities

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (EBM) for study frequency of this equation. By comparemodified homotopy perturbation method with numerical solution we find that this modified homotopyperturbation method works very well for the wide range of time and boundary conditions fornonlinear oscillator, and comparison of the result obtained using this method for frequency with thoseobtained by Energy balance method reveals that the former is very effective and convenient. The newmodified method accelerates the rapid convergence of the solution, reduces the error solution andincreases the validity range for fluctuation and frequency.