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

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.

8 pages, 5 figures, 1 table. Matches accepted MNRAS version. Instructions on code usage available at https://github.com/matthewholman/rebound/tree/master/examples/encke_hh

References in corpus (4)

• Hybrid Symplectic Integrators for Planetary Dynamics
• Time-symmetric integration in astrophysics
• Are long-term $N$-body simulations reliable?
• Should $N$-body integrators be symplectic everywhere in phase space?

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• Significant improvement in planetary system simulations from statistical averaging