Numerical precession in variational discretizations of the Kepler problem
Numerical Analysis
2016-05-20 v2
Abstract
Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center. In numerical simulations of this system one often observes a slight precession of the ellipse around the gravitational center. Using the Lagrangian structure of modified equations and a perturbative version of Noether's theorem, we provide leading order estimates of this precession for the implicit MidPoint rule (MP) and the St\"ormer-Verlet method (SV). Based on those estimates we construct some new numerical integrators that perform significantly better than MP and SV on the Kepler problem.
Cite
@article{arxiv.1602.01049,
title = {Numerical precession in variational discretizations of the Kepler problem},
author = {Mats Vermeeren},
journal= {arXiv preprint arXiv:1602.01049},
year = {2016}
}