  In this paper we present a numerical scheme for stochastic differential
equations based upon the Wiener chaos expansion. The approximation of a square
integrable stochastic differential equation is obtained by cutting off the
infinite chaos expansion in chaos order and in number of basis elements. We
derive an explicit upper bound for the $L^2$ approximation error associated
with our method. The proofs are based upon an application of Malliavin
calculus.
