EnckeHH: an integrator for gravitational dynamics with a dominant mass that achieves optimal error behaviour

TL;DR

EnckeHH is a new high-precision integrator for gravitational systems that maintains optimal error growth, outperforming existing methods like IAS15 and WHCKL in accuracy for fixed step sizes.

Contribution

It introduces EnckeHH, a novel integrator based on Encke's equations, achieving superior accuracy and error control in orbital simulations of perturbed Keplerian systems.

Findings

EnckeHH is 3.5 orders of magnitude more accurate than IAS15 in long-term Solar System integration.

EnckeHH maintains optimal roundoff error growth through advanced numerical techniques.

It surpasses existing integrators like IAS15 and WHCKL in fixed step size accuracy.

Abstract

We present EnckeHH, a new, highly accurate code for orbital dynamics of perturbed Keplerian systems such as planetary systems or galactic centre systems. It solves Encke's equations of motion, which assume perturbed Keplerian orbits. By incorporating numerical techniques, we have made the code follow optimal roundoff error growth. In a $10^ {12}$ day integration of the outer Solar System, EnckeHH was $3.5$ orders of magnitude more accurate than IAS15 in a fixed time step test. Adaptive steps are recommended for IAS15. Through study of efficiency plots, we show that EnckeHH reaches significantly higher accuracy than the Rebound integrators IAS15 and WHCKL for fixed step size.