Some new approaches to duffing equation with strongly and high order nonlinearity (I) linearized perturbation technique

Abstract

A new perturbation technique called linearized perturbation method is proposed. Contrary to the traditional perturbation techniques, the unperturbed equation is obtained by linearizing the original nonlinear equation, not by setting ε = 0. The obtained results are valid not only for small parameters, but also for very large values of ε. The period for the Duffing equation with 5th order nonlinearity is of very high accuracy, the maximal relative error in the total region 0 ≤ ε < ∞ is less than 0.08%.