Solving random diffusion models with nonlinear perturbations by the Wiener-Hermite expansion method

This paper deals with the construction of approximate series solutions of random nonlinear diffusion equations where nonlinearity is considered by means of a frank small parameter and uncertainty is introduced through white noise in the forcing term. For the simpler but important case in which the diffusion coefficient is time independent, we provide a Gaussian approximation of the solution stochastic process by taking advantage of the Wiener-Hermite expansion together with the perturbation method. In addition, approximations of the main statistical functions associated with a solution, such as the mean and variance, are computed. Numerical values of these functions are compared with respect to those obtained by applying the Runge-Kutta second-order stochastic scheme as an illustrative example. (C) 2010 Elsevier Ltd. All rights reserved.