Adv. Appl. Math. Mech., 15 (2023), pp. 737-768.
Published online: 2023-02
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0073}, url = {http://global-sci.org/intro/article_detail/aamm/21448.html} }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.