A piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire

Abstract

In this paper, we introduce a piecewise variational iteration method for treating a nonlinear oscillator of a mass attached to a stretched elastic wire. For the nonlinear oscillator, the present method can produce a good approximation to the exact solution in a very large region, while the standard variational iteration method (VIM) gives a good approximation only in a small region. The numerical results obtained show that the present method does not share the drawback of the standard VIM and can provide very accurate analytical approximate solutions for both small and large values of the oscillation amplitude and parameter.