  In this paper the numerical approximation of stochastic differential
equations satisfying a global monotonicity condition is studied. The strong
rate of convergence with respect to the mean square norm is determined to be
$\frac{1}{2}$ for the two-step BDF-Maruyama scheme and for the backward
Euler-Maruyama method. In particular, this is the first paper which proves a
strong convergence rate for a multi-step method applied to equations with
possibly superlinearly growing drift and diffusion coefficient functions. We
also present numerical experiments for the $\tfrac32$-volatility model from
finance, which verify our results in practice and indicate that the
BDF2-Maruyama method offers advantages over Euler-type methods if the
stochastic differential equation is stiff or driven by a noise with small
intensity.
