A novel second order scheme with one step for forward backward stochastic differential equations

Abstract: In this paper, we present a novel explicit second order scheme with one step for solving the forward backward stochastic differential equations, with the Crank-Nicolson method as a specific instance within our proposed framework. We first present a rigorous stability result, followed by precise error estimates that confirm the proposed novel scheme achieves second-order convergence. The theoretical results for the proposed methods are supported by numerical experiments.