Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines

TL;DR

This paper demonstrates that symplectic correctors can significantly reduce errors caused by adaptive timestepping in orbital simulations, enabling faster and more accurate integrations especially for highly eccentric orbits.

Contribution

It introduces a novel use of symplectic correctors to mitigate errors in adaptive timestepping routines, improving efficiency and accuracy in orbital integrations.

Findings

Error in energy and angular momentum is negligible with correctors

Algorithm is nearly as accurate as fixed-step routines

Significantly faster for highly eccentric, large semimajor axis orbits

Abstract

It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here we show that when altering the timestep symplectic correctors can be used to reduce this error to a negligible level. Furthermore, these correctors can also be employed to avoid a large error introduction when changing the Hamiltonian's partitioning. We have constructed a numerical integrator using this technique that is nearly as accurate as widely used fixed-step routines. In addition, our algorithm is drastically faster for integrations of highly eccentricitic, large semimajor axis orbits, such as those found in the Oort Cloud.