Abstract:

The study of nonlinear oscillator is important issue in the development of theory of dynamical system. One of the newest analytical methods to solve nonlinear equations is the application of both homotopy perturbation and variational iteration techniques. Homotopy perturbation method (HPM), which does not need small parameters is compared with variational iteration method (VIM) and both of them compare with numerical solution in the field of sub-harmonic nonlinear oscillation. The justification for using this method is the difficulties and limitations of perturbation and homotopy when used individually. In this paper, homotopy perturbation method and varational iteration method are used to solve for periodic method for sub-harmonic of nonlinear oscillation. After solving the equations, we found effect of each parameter and the best value for solving equations was   ε=0.1,λ=1,α=0.1,β=1.

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