One order numerical scheme for forward-backward stochastic differential equations

A one order numerical scheme based on the four step scheme developed by Ma et¿al. for the adapted solutions to a class of forward-backward stochastic differential equations is proposed and analyzed. For the decoupling quasilinear parabolic equations, a new kind of characteristics and finite difference method is used. While for the decoupled forward SDE, we use the Milstein scheme.