Reliable event detection for Taylor methods in astrodynamics

ABSTRACT We present a novel approach for the detection of events in systems of ordinary differential equations. The new method combines the unique features of Taylor integrators with state-of-the-art polynomial root finding techniques to yield a novel algorithm, ensuring strong event detection guara...

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Bibliographic Details
Published inMonthly notices of the Royal Astronomical Society Vol. 513; no. 4; pp. 4833 - 4844
Main Authors Biscani, Francesco, Izzo, Dario
Format Journal Article
LanguageEnglish
Published Oxford University Press 23.05.2022
Subjects
gravitation
methods: numerical
celestial mechanics
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Summary:ABSTRACT We present a novel approach for the detection of events in systems of ordinary differential equations. The new method combines the unique features of Taylor integrators with state-of-the-art polynomial root finding techniques to yield a novel algorithm, ensuring strong event detection guarantees at a modest computational overhead. Detailed tests and benchmarks focused on problems in astrodynamics and celestial mechanics (such as collisional N-body systems, spacecraft dynamics around irregular bodies accounting for eclipses, computation of Poincaré sections, etc.) show how our approach is superior in both performance and detection accuracy to strategies commonly employed in modern numerical integration works. The new algorithm is available in our open source Taylor integration package heyoka.
ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/stac1092