TY - JOUR T1 - Sinc-Multistep Schemes for Forward Backward Stochastic Differential Equations AU - Wang , Xu AU - Zhao , Weidong JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 737 EP - 768 PY - 2023 DA - 2023/02 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0073 UR - https://global-sci.org/intro/article_detail/aamm/21448.html KW - Forward backward stochastic differential equations, multistep schemes, Sinc quadrature rule, error estimates. AB -

In this work, by combining the multistep discretization in time and the Sinc quadrature rule for approximating the conditional mathematical expectations, we will propose new fully discrete multistep schemes called “Sinc-multistep schemes” for forward backward stochastic differential equations (FBSDEs). The schemes avoid spatial interpolations and admit high order of convergence. The stability and the $K$-th order error 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 the effectiveness, stability, and high order of convergence of the proposed schemes.