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

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. 
@article{ZVMMF_2015_55_8_a1,
     author = {G. G. Elenin and T. G. Elenina},
     title = {A one-parameter family of difference schemes for the numerical solution of the {Keplerian} problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1292--1298},
     publisher = {mathdoc},
     volume = {55},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a1/}
}
TY  - JOUR
AU  - G. G. Elenin
AU  - T. G. Elenina
TI  - A one-parameter family of difference schemes for the numerical solution of the Keplerian problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1292
EP  - 1298
VL  - 55
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a1/
LA  - ru
ID  - ZVMMF_2015_55_8_a1
ER  - 
%0 Journal Article
%A G. G. Elenin
%A T. G. Elenina
%T A one-parameter family of difference schemes for the numerical solution of the Keplerian problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1292-1298
%V 55
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a1/
%G ru
%F ZVMMF_2015_55_8_a1
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/