Modified Hermite integrators of arbitrary order

Abstract

ABSTRACT 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 minimizes integrated errors in the argument of periapsis for any such integrator. In addition to providing an alternate derivation of the modified corrector for the fourth-order Hermite integrator, we focus on improved correctors for the sixth- and eighth-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.