| Abstract: |
| For the $\theta$-scheme and the Crank-Nicolson scheme for solving backward stochastic differential equations (BSDEs), by using the Adomian decomposition for the nonlinear generator of BSDEs and by introducing a system of new BSDEs, we theoretically obtain their asymptotic expansions. Based on the expansions, we propose extrapolation methods of the two schemes for solving FBSDEs. Our numerical tests verify our theoretical conclusions, and show that the extrapolation algorithms are very efficient and have the capacity of solving complicated physical problems. |
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