Euler-Maruyama Numerical solution of some stochastic functional differential equations

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $du(x,t) = f(x,t,u_t)dt + g(x,t,u_t)dB(t),~ t>0$ with initial data $u(x,0)= u_0(x)=xi in L^p_{F_0}([- au,0];R^n)$ Here $x in R^n$ ($R^n$ is the $ u$-dimenional Euclidean space), $f: C([- au,0]; R^n ) imes R^{ u + 1} ightarrow R^n$ $g: C([- au,0];R^n) imes R^{ u + 1} ightarrow R^{n imes m } u(x,t)in R^n$ for each $t$, $u_t = {u(x,t+ heta ):- auleq hetaleq 0}in C([- au,0];R^n)$ and $B(t)$ is an m-dimensional Brownian motion.