We present heyoka, a new, modern and general-purpose implementation of Taylor's integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational problems in astrodynamics and celestial mechanics show how our general-purpose integrator is competitive with and often superior to state-of-the-art specialised symplectic and non-symplectic integrators in both speed and accuracy. In particular, we show how Taylor methods are capable of satisfying Brouwer's law for the conservation of energy in long-term integrations of planetary systems over billions of dynamical timescales. We also show how close encounters are modelled accurately during simulations of the formation of the Kirkwood gaps and of Apophis' 2029 close encounter with the Earth (where heyoka surpasses the speed and accuracy of domain-specific methods). heyoka can be used from both C++ and Python, and it is publicly available as an open-source project.
翻译:我们展示了泰勒融合法的新型、现代和通用的“heyoka”,用于对普通差异方程式进行数字化解决。详细的数字测试侧重于在天体动力学和天体力学方面困难的高精度重力问题。详细的数字测试表明,我们的通用集成器在速度和准确性两方面都与最先进的专门性共振和非共振集成器具有竞争力,而且往往优于最先进的非共振和非共振集成器。我们尤其展示了泰勒方法如何能够在行星系统超过数十亿个动态时标的长期集成中满足Brouwer的节能法。我们还展示了在模拟形成柯克伍德差距和阿波菲斯2029年与地球的近距离时(赫诺卡超越了特定域方法的速度和准确性)时,如何准确地模拟了近距离接触。Heyoka方法可以从C++和Python两种角度使用,并公开作为开放源项目。