论文标题
修改了任意秩序的HERMITE集成商
Modified Hermite Integrators of Arbitrary Order
论文作者
论文摘要
我们提出了一个由任意秩序的经过修改的HERMITE集成商家族，具有卓越的行为，以整合开普勒和近循环轨道。在叙述了任意顺序的Hermite N体积分器的推导之后，我们得出了一个校正器表达式，该表达式最小化了任何此类集成符的围periapiss参数中的综合误差。除了为第四阶Hermite Integrator提供修改后的校正器的替代推导外，我们还专注于改进的校正器，用于先前在文献中出现的第六阶和8阶集成器。我们提供了一组数字示例，发现高阶方案即使考虑到浮点操作的成本略高，也可以提高性能。本文介绍的算法对以中心电位（例如行星系统和星系中心）为主的系统具有希望。可以修改任何订单的现有HERMITE集成商，以最少的努力使用此处提供的表达式。因此，本文提出的计划可以轻松地在大规模的并行体系结构上实施。
We present a family of modified Hermite integrators of arbitrary order possessing superior behaviour for the integration of Keplerian and near-Keplerian orbits. After recounting the derivation of Hermite N-body integrators of arbitrary order, we derive a corrector expression that minimises integrated errors in the argument of periapsis for any such integrator. In addition to providing an alternate derivation of the modified corrector for the 4th-order Hermite integrator, we focus on improved correctors for the 6th- and 8th-order integrators previously featured in the literature. We present a set of numerical examples and find that the higher-order schemes improve performance, even when considering their slightly higher cost in floating point operations. The algorithms presented herein hold promise for systems dominated by central potentials, such as planetary systems and the centres of galaxies. Existing Hermite integrators of any order can be modified to use the expressions presented here with minimal effort. Accordingly the schemes presented herein can be easily implemented on massively parallel architectures.
