Geodesic
A one-parameter family of difference schemes for the numerical solution of the Keplerian problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1292-1298 
G. G. Elenin; T. G. Elenina. A one-parameter family of difference schemes for the numerical solution of the Keplerian problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1292-1298. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A family of numerical methods for solving the Keplerian problem is proposed. All the methods in this family are symplectic. They preserve the angular momentum, the total energy, the components of the Laplace–Runge–Lenz vector, and the phase volume. The underlying idea is an exact linearization of the problem based on the Levi–Civita transformation and two-stage symmetricsymplectic Runge–Kutta methods.

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