Solving random diffusion models with nonlinear perturbations by the WienerHermite 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 WienerHermite 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 RungeKutta second-order stochastic scheme as an illustrative example.
wienerhermite expansion perturbation method random differential equation