Higher Order Methods for Differential Inclusions
Classical Analysis and ODEs
2012-06-29 v1 Numerical Analysis
Abstract
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time interval. We provide formulas for the local error based on Lipschitz constants and bounds on higher-order derivatives. The method is based on a Fliess-like expansion, and extends previous results by providing error estimates which are valid for all possible inputs.
Cite
@article{arxiv.1206.6563,
title = {Higher Order Methods for Differential Inclusions},
author = {Sanja Gonzalez Zivanovic and Pieter Collins},
journal= {arXiv preprint arXiv:1206.6563},
year = {2012}
}