Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations

Abstract

This is the second part of our series papers on the deferred correction method for forward backward stochastic differential equations. In this work, we extend our previous work in Tang et al. (Numer Math Theory Methods Appl 10(2):222–242, 2017) to solve second-order forward backward stochastic differential equations (2FBSDEs). More precisely, we propose a class of explicit deferred correction schemes for 2FBSDEs. The key feature is that the simple Euler scheme is used as an initialization. Then, by a simple deferred correction iteration scheme, one can obtain an approximated solution with very high accuracy. Yet in each iteration, the computational complexity is always comparable to the Euler solver. Numerical examples are presented to show the effectiveness of the proposed scheme. We believe that the scheme proposed in this work is promising when dealing with 2FBSDEs in moderate dimensions.