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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 6, Pages 895–913 (Mi zvmmf10703)  

This article is cited in 1 scientific paper (total in 1 paper)

Testing of adaptive symplectic conservative numerical methods for solving the Kepler problem

G. G. Elenin, T. G. Elenina

Moscow State University, Moscow, Russia

Abstract: The properties of a family of new adaptive symplectic conservative numerical methods for solving the Kepler problem are examined. It is shown that the methods preserve all first integrals of the problem and the orbit of motion to high accuracy in real arithmetic. The time dependences of the phase variables have the second, fourth, or sixth order of accuracy. The order depends on the chosen values of the free parameters of the family. The step size in the methods is calculated automatically depending on the properties of the solution. The methods are effective as applied to the computation of elongated orbits with an eccentricity close to unity.

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

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0065-2014-0031


DOI: https://doi.org/10.7868/S0044466918060054

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:6, 863–880

Bibliographic databases:

UDC: 519.62
Received: 25.04.2017

Citation: G. G. Elenin, T. G. Elenina, “Testing of adaptive symplectic conservative numerical methods for solving the Kepler problem”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 895–913; Comput. Math. Math. Phys., 58:6 (2018), 863–880

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. Elenin G.G. Elenina T.G., “Parametrization of the Solution of the Kepler Problem and New Adaptive Numerical Methods Based on This Parametrization”, Differ. Equ., 54:7 (2018), 911–918  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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