, Volume 67, Issue 3, pp 315-344

Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations

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A general method for constructing high-order approximation schemes for Hamilton-Jacobi-Bellman equations is given. The method is based on a discrete version of the Dynamic Programming Principle. We prove a general convergence result for this class of approximation schemes also obtaining, under more restrictive assumptions, an estimate in \(L^\infty\) of the order of convergence and of the local truncation error. The schemes can be applied, in particular, to the stationary linear first order equation in \({\Bbb R}^n\) . We present several examples of schemes belonging to this class and with fast convergence to the solution.

Received July 4, 1992 / Revised version received July 7, 1993