A Priori Adaptive Numerical Methods for Estimating Blow-up Times of Autonomous ODEs
Numerical Analysis
2026-03-16 v1 Numerical Analysis
Abstract
We present effective a priori adaptive numerical methods for estimating the blow-up time for solutions of autonomous ODEs. The novelty of our approach is to base our adaptive steps on the sensitivity of an auxiliary hitting time. We provide results on the theoretical error rates, and show that there is a benefit in terms of computational effort in choosing our adaptive algorithm over alternative approaches. Numerical experiments support our theoretical results and show how the methods perform in practice.
Keywords
Cite
@article{arxiv.2603.12957,
title = {A Priori Adaptive Numerical Methods for Estimating Blow-up Times of Autonomous ODEs},
author = {Håkon Hoel and Johannes Vincent Meo},
journal= {arXiv preprint arXiv:2603.12957},
year = {2026}
}