  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.
