Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations (Advances in Applied Mathematics and Mechanics, 2023)
In this work, by combining the multistep discretization in time and the Sincquadrature rule for approximating the conditional mathematical expectations, we willpropose new fully discrete multistep schemes called “Sinc-multistep schemes” for forward backward stochastic differential equations (FBSDEs). The schemes avoid spatialinterpolations and admit high order of convergence. The stability and the $K$-th ordererror estimates in time for the $K$-step Sinc multistep schemes are theoretically proved $(1≤K≤6).$ This seems to be the first time for analyzing fully time-space discrete multistep schemes for FBSDEs. Numerical examples are also presented to demonstrate theeffectiveness, stability, and high order of convergence of the proposed schemes.