Iteration perturbation method for strongly nonlinear oscillations

In this paper, the author proposes a new perturbation technique coupling wi th iteration method, yielding a powerful mathematical tool for an analytica l solution of nonlinear equations. The obtained results are valid not only for weakly nonlinear problems but also for strongly nonlinear ones. Further more, the approximate solutions are valid for the whole solution domain, an d even the first-step iteration leads to high accuracy. Some examples are g iven to illustrate its effectiveness.