Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions
Mathematical Physics
2009-11-10 v3 Astrophysics
math.MP
Computational Physics
Abstract
We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth accuracy in the periodic energy. We study the 1-D harmonic oscillator and the 2-D Kepler problem in great details, and compare the effectiveness of some recent fourth order algorithms.
Cite
@article{arxiv.math-ph/0411086,
title = {Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions},
author = {S. R. Scuro and S. A. Chin},
journal= {arXiv preprint arXiv:math-ph/0411086},
year = {2009}
}
Comments
Submitted to Phys. Rev. E, 29 Pages