TY - JOUR
T1 - Richardson Extrapolation of the Crank-Nicolson Scheme for Backward Stochastic Differential Equations
AU - Xu , Yafei
AU - Zhao , Weidong
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 268
EP - 294
PY - 2024
DA - 2024/04
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1011
UR - https://global-sci.org/intro/article_detail/ijnam/23027.html
KW - Backward stochastic differential equations, Crank-Nicolson scheme, Adomian decomposition, Richardson extrapolation, asymptotic error expansion.
AB - <p style="text-align: justify;">In this work, we consider Richardson extrapolation of the Crank-Nicolson (CN)
scheme for backward stochastic differential equations (BSDEs). First, applying the Adomian
decomposition to the nonlinear generator of BSDEs, we introduce a new system of BSDEs. Then
we theoretically prove that the solution of the CN scheme for BSDEs admits an asymptotic
expansion with its coefficients the solutions of the new system of BSDEs. Based on the expansion,
we propose Richardson extrapolation algorithms for solving BSDEs. Finally, some numerical tests
are carried out to verify our theoretical conclusions and to show the stability, efficiency and high
accuracy of the algorithms.</p>