This article is cited in 6 papers

A one-parameter family of difference schemes for the numerical solution of the Keplerian problem

G. G. Elenin, T. G. Elenina

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: 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.

Key words: Hamiltonian systems, symplecticity, invertibility, motion integrals, Runge–Kutta methods, Keplerian problem.

UDC: 519.62

Received: 26.03.2015

DOI: 10.7868/S0044466915080074

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:8, 1264–1269

Bibliographic databases:

• 
• 
• 
• 
•