  Recently, a new class of second order Runge-Kutta methods for It\^o
stochastic differential equations with a multidimensional Wiener process was
introduced by R\"o{\ss}ler. In contrast to second order methods earlier
proposed by other authors, this class has the advantage that the number of
function evaluations depends only linearly on the number of Wiener processes
and not quadratically. In this paper, we give a full classification of the
coefficients of all explicit methods with minimal stage number. Based on this
classification, we calculate the coefficients of an extension with minimized
error constant of the well-known RK32 method to the stochastic case. For three
examples, this method is compared numerically with known order two methods and
yields very promising results.
