Modified Hermite Integrators of Arbitrary Order
  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.
