Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper deals with a numerical scheme to approximate the mth moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random function and the transport velocity is a random variable. The scheme is based on local Riemann problem solutions and Godunov's method. We show that the scheme is stable and consistent with an advective-diffusive equation. Numerical examples are added to illustrate our approach. (C) 2008 Elsevier Inc. All rights reserved.2271985418550Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [140406/2004-2]