A Monotone Scheme For High Dimensional Fully Nonlinear PDEs

In this paper we propose a feasible numerical scheme for high dimensional fully nonlinear parabolic PDEs, which includes the quasi-linear PDE associated with a cou-pled FBSDE as a special case. Our scheme weakens a critical constraint imposed by Fahim, Touzi å'ŒWarin [Ann. Appl. Probab,21(2011) pp.1322-1364], especially when the generator of the PDE depends only on the diagonal terms of the hessian matrix. Several numerical examples, up to dimension 12, are reported.