application of the homotopy perturbation method to solve nonlinear equations arising in oscillatory systems

In this research, the application of the homotopy perturbation method to solve nonlinear equations arising in oscillatory systems is investigated. in this way, the performance of the homotopy perturbation method (hpm) is compared with the numerical methods to find the solutions of nonlinear equations in the vibration field. to this end, the duffing&-holmes oscillatory model with nonlinear terms is regarded and solved by the hpm method. in order to validate the obtained solution by the hpm, the answers are compared with those of numerical methods. the results clearly depict that the homotopy perturbation method, without needing to small parameters, could present the answers near to the exact solutions and also to the numerical one.