A High Order Finite Difference Method for Random Parabolic Partial Differential Equations

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has these properties. Finally a numerical example is solved to illustrate the scheme of analysis.