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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 8, Pages 1292–1298
DOI: https://doi.org/10.7868/S0044466915080074 (Mi zvmmf10244) 		 
This article is cited in 6 scientific papers (total 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
Full-text PDF (89 kB) Citations (6)
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DOI: https://doi.org/10.7868/S0044466915080074
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.
Received: 26.03.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 8, Pages 1264–1269
DOI: https://doi.org/10.1134/S0965542515080072
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: G. G. Elenin, T. G. Elenina, “A one-parameter family of difference schemes for the numerical solution of the Keplerian problem”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1292–1298; Comput. Math. Math. Phys., 55:8 (2015), 1264–1269
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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