Approximate Solution of the Stochastic Nonlinear Oscillator‎

In this paper, we consider the nonlinear equations with the additive white noise, which are commonly impossible to be solved by an analytical procedure. The Block-Pulse functions as basic functions are proposed to solve these equations. In order to investigate the validity of this method, we used the Adomian decomposition method to approximate the solution of the stochastic Duffing equations. The results reveal that the proposed method is very effective.