  In this paper, we derive fully implementable first order time-stepping
schemes for McKean--Vlasov stochastic differential equations (McKean--Vlasov
SDEs), allowing for a drift term with super-linear growth in the state
component. We propose Milstein schemes for a time-discretised interacting
particle system associated with the McKean--Vlasov equation and prove strong
convergence of order 1 and moment stability, taming the drift if only a
one-sided Lipschitz condition holds. To derive our main results on strong
convergence rates, we make use of calculus on the space of probability measures
with finite second order moments. In addition, numerical examples are presented
which support our theoretical findings.
