(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
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 kth order (1k6) fully discrete explicit multistep schemes. Numerical tests are presented to demonstrate the strong stability, high accuracy, and high efficiency of the explicit schemes.