ABSTRACT
ABSTRACT: The Wiener-Hermite expansion and perturbation technique (WHEP) showed a great efficiency in introducing the average and covariance solution for perturbative stochastic differential equations This technique has been greatly extended by the use of homotopy perturbation to yield what is called Homotopy WHEP. In this technique the homotopy technique replaces the ordinary perturbation technique which enables the application of the technique on non-perturbative problems. This means that an efficient algorithm can introduce an average and covariance solution for almost general stochastic differential equations. The solution proposed by the algorithm is sufficient for many applicants, e.g. engineers, to better handle a random system described by a stochastic differential equation when having an average solution and a variance as a measure of an error in the average solution. Better design is obtained when having this knowledge. In this paper, the algorithm is particularly applied on some nonlinear stochastic differential equations.
