Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...303..940h&link_type=abstract
Astronomy and Astrophysics, v.303, p.940
Astronomy and Astrophysics
Astrophysics
4
Methods: Numerical, Celestial Mechanics, Ephemerides, Planets And Satellites
Scientific paper
The 10th-order Gauss-Jackson backward difference numerical integration method and the Runge-Kutta-Nystroem RKN12(10)17M method were applied to the equations of motion and variational equations of the Saturnian satellite system. We investigated the effect of step-size on the stability of the Gauss-Jackson method in the two distinct cases arising from the inclusion or exclusion of the corrector cycle in the integration of the variational equations. In the predictor-only case, we found that instability occurred when the step-size was greater than approximately 1/76 of the orbital period of the innermost satellite. In the predictor-corrector case, no such instability was observed, but larger step-sizes yield significant loss in accuracy. By contrast, the investigation of the Runge-Kutta-Nystroem method showed that it allows the use of much larger step-sizes and can still obtain high-accuracy results, thus making evident the superiority of the method for the integration of planetary satellite systems.
Hadjifotinou K. G.
Harper Devin
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