Year: 2023
Author: Xu Wang, Weidong Zhao
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 737–768
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0073
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 737–768
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Forward backward stochastic differential equations multistep schemes Sinc quadrature rule error estimates.