TY - JOUR
T1 - High-Efficiency Explicit Multistep Schemes for Coupled Second-Order FBSDEs
AU - Li , Bo
AU - Zhao , Weidong
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 322
EP - 347
PY - 2025
DA - 2025/10
SN - 18
DO - http://doi.org/10.4208/aamm.OA-2024-0273
UR - https://global-sci.org/intro/article_detail/aamm/24529.html
KW - Explicit multistep scheme, second-order forward backward stochastic differential equations, recursive approximation, Sinc quadrature rule.
AB - <p style="text-align: justify;">In this work, by introducing a new family of recursively defined processes, we propose new explicit multistep schemes for coupled second-order forward backward stochastic differential equations. The explicit schemes avoid calculating the conditional mathematical expectations of the generator $f$ and calculate the required values of $f$ explicitly and accurately. By combining the Sinc quadrature rule for approximating the conditional expectations, we further propose the $k$th order ($1\le k\le 6$) fully discrete explicit multistep schemes. Numerical tests are presented to demonstrate the strong stability, high accuracy, and high efficiency of the explicit schemes.</p>