Testing of Adaptive Symplectic Conservative Numerical Methods for Solving the Kepler Problem

  • G. G. EleninEmail author
  • T. G. EleninaEmail author


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.


Hamiltonian systems symplecticity invertibility integrals of motion Runge–Kutta methods Kepler problem. 



This work was supported in part by Moscow State University and the Scientific Research Institute for System Analysis of the Russian Academy of Sciences, project no. 0065-2014-0031.


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and Cybernetics, Moscow State UniversityMoscowRussia
  2. 2.Scientific Research Institute for System Analysis, Federal Research Center, Russian Academy of SciencesMoscowRussia
  3. 3.Faculty of Physics, Moscow State UniversityMoscowRussia

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