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 Poincare' 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.

翻译：新的方法将泰勒集成商的独特特征与最先进的多元根基调查技术结合起来,产生一种新奇算法,确保适度的计算间接费用能保证对事件探测的保证。 详细的测试和基准侧重于天体动力学和天体力学(例如碰撞的N-体系统、围绕非正常日蚀核算机体的航天器动态、Poincare部分的计算等)的问题。 新的方法表明我们的方法在性能和探测准确性方面如何优于现代数字集成工程通常采用的战略。 新的算法可以在我们开放源的泰勒集成软件中找到。