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

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.