  We propose some numerical schemes for forward-backward stochastic
differential equations (FBSDEs) based on a new fundamental concept of
transposition solutions. These schemes exploit time-splitting methods for the
variation of constants formula of the associated partial differential equations
and a discrete representation of the transition semigroups. The convergence of
the schemes is established for FBSDEs with uniformly Lipschitz drivers, locally
Lipschitz and maximal monotone drivers. Numerical experiments are presented for
several nonlinear financial derivative pricing problems to demonstrate the
adaptivity and effectiveness of the new schemes. The ideas here can be applied
to construct high-order schemes for FBSDEs with general Markov forward
processes.
