Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines

Details Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines

2010-11-16

arxiv.org/abs/1011.3830v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

Accepted to AJ, 29 pages, 8 figures

Scientific paper

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.

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