  This is one of our series papers on multistep schemes for solving forward
backward stochastic differential equations (FBSDEs) and related problems. Here
we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu
and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751.] to solve the
second order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that
the Euler method is used to discrete the forward SDE, which dramatically
reduces the entire computational complexity. Moreover, it is shown that the
usual quantities of interest (e.g., the solution tuple $(Y_t, Z_t, A_t,
\Gamma_t)$ in the 2FBSDEs) are still of high order accuracy. Several numerical
examples are given to show the effective of the proposed numerical schemes.
Applications of our numerical schemes for stochastic optimal control problems
are also presented.
