TY - JOUR
T1 - ODE-Based Multistep Schemes for Backward Stochastic Differential Equations
AU - Fang , Shuixin
AU - Zhao , Weidong
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1053
EP - 1086
PY - 2023
DA - 2023/11
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2023-0060 
UR - https://global-sci.org/intro/article_detail/nmtma/22123.html
KW - Backward stochastic differential equation, parabolic partial differential equation, strong stability preserving, linear multistep scheme, high order discretization.
AB - <p style="text-align: justify;">In this paper, we explore a new approach to design and analyze numerical
schemes for backward stochastic differential equations (BSDEs). By the nonlinear
Feynman-Kac formula, we reformulate the BSDE into a pair of reference ordinary
differential equations (ODEs), which can be directly discretized by many standard
ODE solvers, yielding the corresponding numerical schemes for BSDEs. In particular,
by applying strong stability preserving (SSP) time discretizations to the reference
ODEs, we can propose new SSP multistep schemes for BSDEs. Theoretical analyses
are rigorously performed to prove the consistency, stability and convergency of the
proposed SSP multistep schemes. Numerical experiments are further carried out to
verify our theoretical results and the capacity of the proposed SSP multistep schemes
for solving complex associated problems.</p>