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：针对含时一阶Hamilton--Jacobi--Bellman方程，我们提出一种高阶数值格式。具体而言，我们将半拉格朗日格式与中心加权非振荡重构相结合。对于状态和时间无关的哈密顿量情形，我们证明了其收敛性。文中给出了一维和二维空间中的数值模拟结果，并针对更一般的状态与时间相关哈密顿量进行了实验，结果表明相较于采用加权非振荡重构的耦合半拉格朗日格式，本方法在CPU时间节省方面具有显著优势。