  By using the stochastic particle method, the truncated Euler-Maruyama (TEM)
method is proposed for numerically solving McKean-Vlasov stochastic
differential equations (MV-SDEs), possibly with both drift and diffusion
coefficients having super-linear growth in the state variable. Firstly, the
result of the propagation of chaos in the L^q (q\geq 2) sense is obtained under
general assumptions. Then, the standard 1/2-order strong convergence rate in
the L^q sense of the proposed method corresponding to the particle system is
derived by utilizing the stopping time analysis technique. Furthermore,
long-time dynamical properties of MV-SDEs, including the moment boundedness,
stability, and the existence and uniqueness of the invariant probability
measure, can be numerically realized by the TEM method. Additionally, it is
proven that the numerical invariant measure converges to the underlying one of
MV-SDEs in the L^2-Wasserstein metric. Finally, the conclusions obtained in
this paper are verified through examples and numerical simulations.
