On the non-existence of higher order monotone approximation schemes for HJB equations

doi:10.1016/j.aml.2015.08.005

Applied Mathematics Letters

Volume 52, February 2016, Pages 53-57

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Abstract

In this work we present a result on the non-existence of monotone, consistent linear discrete approximation of order higher than 2. This is an essential ingredient, if we want to solve numerically nonlinear and particularly Hamilton–Jacobi–Bellman (HJB) equations.

Keywords

Hamilton–Jacobi–Bellman equation

Monotone numerical schemes

Order of consistency