@Article{IJNAM-21-2,
author = {Yafei, Xu and Zhao, Weidong},
title = {Richardson Extrapolation of the Crank-Nicolson Scheme for Backward Stochastic Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {2},
pages = {268--294},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1011},
url = {https://global-sci.com/article/91058/richardson-extrapolation-of-the-crank-nicolson-scheme-for-backward-stochastic-differential-equations}
}