High-order Combined Multi-step Scheme for Solving Forward Backward Stochastic Differential Equations

Abstract In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we propose a new multi-step scheme by adopting the high-order method Zhao et al. (SIAM J. Sci. Comput., 36(4): A1731-A1751, 2014) with combination technique. Two reference ordinary equations containing conditional expectations and their derivatives are derived from component. These approximated using finite difference methods combinations. The resulting is semi-discretization temporal direction involving expectations, which solved Gaussian quadrature rules polynomial interpolations on spatial grids. Our proposed allows higher convergence rate up ninth order, more efficient. Finally, provide numerical illustration of method.