  We present a new efficient computational approach for time-dependent
first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a
time-implicit Eulerian discretization, the numerical scheme is unconditionally
stable, but discretized equations for each time-slice are coupled and
non-linear. We show that the same system can be re-interpreted as a
discretization of a static Hamilton-Jacobi-Bellman PDE on the same physical
domain. The latter was shown to be ``causal' in [Vladimirsky 2006], making fast
(non-iterative)methods applicable. The implicit discretization results in
higher computational cost per time slice compared to the explicit time
marching. However, the latter is subject to a CFL-stability condition, and the
implicit approach becomes significantly more efficient whenever the accuracy
demands on the time-step are less restrictive than the stability. We also
present a hybrid method, which aims to combine the advantages of both the
explicit and implicit discretizations. We demonstrate the efficiency of our
approach using several examples in optimal control of isotropic fixed-horizon
processes.
