  We present a numerical method for the approximation of solutions for the
class of stochastic differential equations driven by Brownian motions which
induce stochastic variation in fixed directions. This class of equations arises
naturally in the study of population processes and chemical reaction kinetics.
We show that the method constructs paths that are second order accurate in the
weak sense. The method is simpler than many second order methods in that it
neither requires the construction of iterated Ito integrals nor the evaluation
of any derivatives. The method consists of two steps. In the first an explicit
Euler step is used to take a fractional step. This fractional point is then
combined with the initial point to obtain a higher order, trapezoidal like,
approximation. The higher order of accuracy stems from the fact that both the
drift and the quadratic variation of the underlying SDE are approximated to
second order.
