Finite Di erence Methods For Random Partial Di erential Equations

Random partial di erential equations (RPDEs) describe the partial di erential equationsinvolving random inputs which may be a random variable. In this paper, we focus onthe numerical approximation of random parabolic and elliptic partial di erential equations.The main properties of deterministic di erence methods, i.e. consistency, stability and con-vergency, are separately developed for the stochastic case. It is shown that the proposedstochastic di erence schemes for random parabolic and elliptic equations have these proper-ties.