We propose a high order numerical scheme for time-dependent first order Hamilton--Jacobi--Bellman equations. In particular we propose to combine a semi-Lagrangian scheme with a Central Weighted Non-Oscillatory reconstruction. We prove a convergence result in the case of state- and time-independent Hamiltonians. Numerical simulations are presented in space dimensions one and two, also for more general state- and time-dependent Hamiltonians, demonstrating superior performance in terms of CPU time gain compared with a semi-Lagrangian scheme coupled with Weighted Non-Oscillatory reconstructions.

翻译：我们提出了一种适用于时间依赖的一阶Hamilton–Jacobi–Bellman方程的高阶数值格式。具体而言，我们将半拉格朗日格式与中心加权无振荡重构相结合。对于状态和时间无关的哈密顿量情形，我们证明了收敛性结果。文中还给出了空间一维和二维的数值模拟，其中也考虑了更一般的状态和时间相关的哈密顿量，结果表明与结合加权无振荡重构的半拉格朗日格式相比，该方法在CPU时间效率方面具有优越性。