Linearized perturbation technique and its applications to strongly nonlinear oscillators

A new perturbation technique called linearized perturbation method is proposed. Contrary to the traditional perturbation techniques, the unperturbed equations is obtained by linearizing the original nonlinear equation, not by setting ϵ = 0. Therefore, the obtained results are valid not only for small parameter, but also for very large values of ϵ. The present theory is processed as simple as the straightforward expansion, while omits the secular terms completely.