A Forward-Backward Stochastic Algorithm for Quasi-Linear PDEs

We propose a time-space discretization scheme for quasi-linear parabolic PDEs. The algorithm relies on the theory of fully coupled Forward-Backward SDEs, which provides an efficient probabilistic representation of this type of equations. The derivated algorithm holds for strong solutions defined on any interval of arbitrary length. As a bypass product, we obtain a discretization procedure for the underlying FBSDE. In particular, our work provides an alternative to the method described in Douglas, Ma and Protter [DMP96] and weakens the regularity assumptions required in this reference. AMS 2000 Subject Classification. Primary: 65C30. Secondary: 35K55, 60H10, 60H35.