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A modified variational iteration method (MVIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed approach is applied to conservative oscillators. Therefore, highly accurate approximations can be easily obtained. The Duffing and the van der Pol equations are presented to validate the MVIM. Numerical examples show that the presented method is valid for both weakly and strongly nonlinear oscillators. In addition, it reveals that the MVIM is equivalent to a modified Mickens iteration scheme. Furthermore, the MVIM is extended by means of an auxiliary parameter. This parameter provides us with a convenient way to control and adjust the convergence of VIM approximations when necessary.

A Modified Variational Iteration Method for Nonlinear Oscillators