Using neural networks for the derivation of Runge-Kutta-Nyström pairs for integration of orbits

Details Using neural networks for the derivation of Runge-Kutta-Nyström pairs for integration of orbits Using neural networks for the derivation of Runge-Kutta-Nyström pairs for integration of orbits

May 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012newa...17..469t&link_type=abstract

New Astronomy, Volume 17, Issue 4, p. 469-473.

Astronomy and Astrophysics

Astronomy

Scientific paper

In this paper we present Runge-Kutta-Nyström (RKN) pairs of orders 4(3) and 6(4). We choose a test orbit from the Kepler problem to integrate for a specific tolerance. Then we train the free parameters of the above RKN4(3) and RKN6(4) families to perform optimally. For that we form a neural network approach and minimize its objective function using a differential evolution optimization technique. Finally we observe that the produced pairs outperform standard pairs from the literature for Pleiades orbits and Kepler problem over a wide range of eccentricities and tolerances.

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