A study on Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Non-linear Oscillators

Abstract

In this paper, the Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyse five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min-Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Hanormic Balance Method (HBM), 4^th order Runge-Kutta Method and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully exerted to a lot of practical engineering and physical problems.