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 $R^n$. We present several examples of schemes belonging to this class and with fast convergence to the solution.

Falcone, M., Ferretti, R. (1994). DISCRETE-TIME HIGH-ORDER SCHEMES FOR VISCOSITY SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS. NUMERISCHE MATHEMATIK, 67(3), 315-344 [10.1007/s002110050031].

### DISCRETE-TIME HIGH-ORDER SCHEMES FOR VISCOSITY SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS

#### Abstract

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 $R^n$. We present several examples of schemes belonging to this class and with fast convergence to the solution.
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Falcone, M., Ferretti, R. (1994). DISCRETE-TIME HIGH-ORDER SCHEMES FOR VISCOSITY SOLUTIONS OF HAMILTON-JACOBI-BELLMAN EQUATIONS. NUMERISCHE MATHEMATIK, 67(3), 315-344 [10.1007/s002110050031].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/144705
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