Approximate analytical solution for certain strongly nonlinear oscillations by the variational iteration method

In this paper, a new kind of analytical method of nonlinear problem solving called variational iteration method is described and used to give approximate solutions for certain strongly oscillations. In this method, a correction functional is constructed via a general Lagrange multiplier which can be identified optimally via the variational theory. The proposed technique does not depend on the small parameter assumption and therefore can overcome the disadvantages and limitations of the perturbation techniques. Some examples reveal that even the first-order approximates are of high accuracy, and are uniformly valid not only for weakly nonlinear systems, but also for strongly ones.