  In this paper we present a perturbative procedure that allows one to
numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations,
for a wide range of memory functions. To illustrate this procedure numerical
results are presented for a classically driven two level atom immersed in a
environment with a simple memory function. It is observed that as the order of
the perturbation is increased the numerical results for the ensembled average
state $\rho_{\rm red}(t)$ approach the exact reduced state found via
Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].
