Discrete time high-order schemes for viscosity solutions of Hamilton- Jacobi-Bellman equations
type: Item
instance of: scholarly article
title: Discrete time high-order schemes for viscosity solutions of Hamilton- Jacobi-Bellman equations
zbMATH Open document ID: 0791.65046
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
review text: The article introduces a class of high-order approximation schemes for first order Hamilton-Jacobi-Bellman equations in \(\mathbb{R}^ n\) (which apply, in particular, to the stationary first order linear equation). The method used to obtain the above schemes is a discrete version of dynamic programming. A general convergence result applies to the schemes in that class: they converge to the viscosity solution whenever the coefficients in the equation are Lipschitz continuous. An estimate in \(L^ \infty\) of the order of convergence and of the local truncation error is proved under more restrictive assumptions. Several examples of these schemes corresponding to the orders of convergence 1, 2 and 4 are presented throughout the paper. The last section contains their detailed analysis and comparison in terms of CPU time and numerical errors on some tests which can have smooth or non smooth solutions.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49L99
zbMATH DE Number: 569103
zbMATH Keywords: optimal control
zbMATH Keywords: numerical examples
zbMATH Keywords: high-order approximation schemes
zbMATH Keywords: first order Hamilton-Jacobi-Bellman equations
zbMATH Keywords: dynamic programming
zbMATH Keywords: convergence
zbMATH Keywords: viscosity solution
author: M. Falcone
author: Roberto Ferretti
reviewed by: M. Falcone
MaRDI profile type: Publication
full work available at URL: s002110050031
OpenAlex ID: W1995720627
DOI: 10.1007/S002110050031
description: scientific article; zbMATH DE number 569103