  In this paper, we present a numerical approach to solve the McKean-Vlasov
equations, which are distribution-dependent stochastic differential equations,
under some non-globally Lipschitz conditions for both the drift and diffusion
coefficients. We establish a propagation of chaos result, based on which the
McKean-Vlasov equation is approximated by an interacting particle system. A
truncated Euler scheme is then proposed for the interacting particle system
allowing for a Khasminskii-type condition on the coefficients. To reduce the
computational cost, the random batch approximation proposed in [Jin et al., J.
Comput. Phys., 400(1), 2020] is extended to the interacting particle system
where the interaction could take place in the diffusion term. An almost half
order of convergence is proved in $L^p$ sense. Numerical tests are performed to
verify the theoretical results.
