  We propose a novel projection-based particle method for solving the
McKean-Vlasov stochastic differential equations. Our approach is based on a
projection-type estimation of the marginal density of the solution in each time
step. The projection-based particle method leads in many situation to a
significant reduction of numerical complexity compared to the widely used
kernel density estimation algorithms. We derive strong convergence rates and
rates of density estimation. The convergence analysis in the case of linearly
growing coefficients turns out to be rather challenging and requires some new
type of averaging technique. This case is exemplified by explicit solutions to
a class of McKean-Vlasov equations with affine drift. The performance of the
proposed algorithm is illustrated by several numerical examples.
