  We propose a new algorithm to approach weakly the solution of a McKean-Vlasov
SDE. Based on the cubature method of Lyons and Victoir 2004, the algorithm is
deterministic differing from the the usual methods based on interacting
particles. It can be parametrized in order to obtain a given order of
convergence. Then, we construct implementable algorithms to solve decoupled
Forward Backward Stochastic Differential equations (FBSDE) of McKean-Vlasov
type, which appear in some stochastic control problems in a mean field
environment. We give two algorithms and show that they have convergence of
order one and two under appropriate regularity conditions.
