In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,;t)=f(x,;t,;u)dt;+;g(x,;t,;u)dW(t);+;sumlimits_{|q|leq2m};A_q(x,;t)D^qu(x,;t)dt$$ where $0;{leq};t;{leq};T,;x;{in};R^{ u}$, ($R^{nu}$ is the $ u$-dimensional Euclidean space). Here $u;{in};R^n$, W(t) is an n-dimensional Brownian motion, $$f;:;R^{n+ u+1};{ ightarrow};R^n,;g;:;R^{n+ u+1};{ ightarrow};R^{n{ imes}n},$$, and $$A_q;:;R^{ u};{ imes};[0,;T];{ ightarrow};R^{n{ imes}n}$$ where ($A_q,;|;q;|{leq};2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{ u};{ imes};[0,;T];and;D^q;=;D^{q_1}_1_{ldots}_{ldots}D^{q_{ u}}_{ u},;D_i;=;{frac{partial}{partial_{x_i}}}$.