2012/06/28 by Sanja Gonzalez Zivanovic, Zivanovic, Sanja Gonzalez, Pieter Collins +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1206.6563
openalex publication_date 2012/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.