  In this paper, we study three numerical schemes for the McKean-Vlasov
equation \[\begin{cases} \;dX_t=b(t, X_t, \mu_t) \, dt+\sigma(t, X_t, \mu_t) \,
dB_t,\: \\ \;\forall\, t\in[0,T],\;\mu_t \text{ is the probability distribution
of }X_t, \end{cases}\] where $X_0$ is a known random variable. Under the
assumption on the Lipschitz continuity of the coefficients $b$ and $\sigma$,
our first result proves the convergence rate of the particle method with
respect to the Wasserstein distance, which extends a previous work [BT97]
established in one-dimensional setting. In the second part, we present and
analyse two quantization-based schemes, including the recursive quantization
scheme (deterministic scheme) in the Vlasov setting, and the hybrid
particle-quantization scheme (random scheme, inspired by the $K$-means
clustering). Two examples are simulated at the end of this paper: Burger's
equation and the network of FitzHugh-Nagumo neurons in dimension 3.
