  We present an error analysis of weak convergence of one-step numerical
schemes for stochastic differential equations (SDEs) with super-linearly
growing coefficients. Following Milstein's weak error analysis on the one-step
approximation of SDEs, we prove a general conclusion on weak convergence of the
one-step discretization of the SDEs mentioned above. As applications, we show
the weak convergence rates for several numerical schemes of half-order strong
convergence, such as tamed and balanced schemes. Numerical examples are
presented to verify our theoretical analysis.
