full
search.png

Search

close.png

Cancel

arrow
Volume 18, Issue 1
High-Efficiency Explicit Multistep Schemes for Coupled Second-Order FBSDEs

Bo Li & Weidong Zhao

DOI: 10.4208/aamm.OA-2024-0273

Adv. Appl. Math. Mech., 18 (2026), pp. 322-347.

Published online: 2025-10

Preview Full PDF 27 245

Cited by

google scholar semantic scholar
Export citation
  • Abstract

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.

  • Keywords

Explicit multistep scheme, second-order forward backward stochastic differential equations, recursive approximation, Sinc quadrature rule.

  • AMS Subject Headings

65C20, 65C30, 60H35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-18-322, author = {Li , Bo and Zhao , Weidong}, title = {High-Efficiency Explicit Multistep Schemes for Coupled Second-Order FBSDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {18}, number = {1}, pages = {322--347}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0273}, url = {http://global-sci.org/intro/article_detail/aamm/24529.html} }
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 -

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.

Li , Bo and Zhao , Weidong. (2025). High-Efficiency Explicit Multistep Schemes for Coupled Second-Order FBSDEs. Advances in Applied Mathematics and Mechanics. 18 (1). 322-347. doi:10.4208/aamm.OA-2024-0273
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard