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 - <p style="text-align: justify;">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.</p>