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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1292–1298 (Mi zvmmf10244)  

This article is cited in 4 scientific papers (total in 4 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.

DOI: https://doi.org/10.7868/S0044466915080074

Full text: PDF file (89 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1264–1269

Bibliographic databases:

UDC: 519.62
Received: 26.03.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 54, no. 7, 2018, 911–918  crossref  mathscinet  isi  scopus
    2. G. G. Elenin, T. G. Elenina, “Adaptive symplectic conservative numerical methods for the Kepler problem”, Differ. Equ., 53:7 (2017), 923–934  crossref  mathscinet  zmath  isi  elib  elib
    3. G. G. Elenin, T. G. Elenina, “Testing of adaptive symplectic conservative numerical methods for solving the Kepler problem”, Comput. Math. Math. Phys., 58:6 (2018), 863–880  mathnet  crossref  crossref  isi  elib
    4. G. G. Elenin, T. G. Elenina, A. A. Ivanov, “O tochnosti odnogo semeistva adaptivnykh simplekticheskikh konservativnykh chislennykh metodov resheniya zadachi Keplera”, Matem. modelirovanie, 33:2 (2021), 55–66  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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