A Priori Adaptive Numerical Methods for Estimating Blow-up Times of Autonomous ODEs
This addresses a specific computational challenge in numerical analysis for researchers working with ODE blow-up phenomena, but appears incremental as it builds on existing adaptive methods.
The paper tackles the problem of estimating blow-up times for autonomous ODEs by developing a priori adaptive numerical methods based on the sensitivity of an auxiliary hitting time, showing benefits in computational effort over alternative approaches with theoretical error rates and numerical experiments.
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.