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We design a class of numerical schemes for backward stochastic differentialequation driven by $G$-Brownian motion ($G$-BSDE), which is related to a fullynonlinear PDE. Based on Peng's central limit theorem, we employ the CLT methodto approximate $G$-distributed. Rigorous stability and convergence analysis arealso carried out. It is shown that the $\theta$-scheme admits a half orderconvergence rate in the general case. In particular, for the case of$\theta_{1}\in[0,1]$ and $\theta_{2}=0$, the scheme can reach first-order inthe deterministic case. Several numerical tests are given to support ourtheoretical results.

Numerical Schemes for Backward Stochastic Differential Equations Driven by $G$-Brownian motion