A Priori Adaptive Numerical Methods for Estimating Blow-up Times of Autonomous ODEs

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Håkon Hoel, Johannes Vincent Meo
DOI: 10.48550/arxiv.2603.12957
Cited by: 0

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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.

Fields of Study & Subjects

Numerical Solvers for Ordinary Differential Equations Singular Perturbation Asymptotics and Difference Schemes Nonlinear Differential Equations Analysis

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 March 2026
Language
EN
Document type
Preprint