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Adaptive symplectic conservative numerical methods for the Kepler problem

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Abstract

We suggest and substantiate a unified form of a family of adaptive conservative numerical methods for the Kepler problem. The family contains methods of the second, fourth, and sixth approximation order as well as an exact method. The methods preserve all the global properties of the exact solution of the problem. The variable time step is chosen automatically depending on the properties of the solution.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    G. G. Elenin & T. G. Elenina

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  1. G. G. Elenin
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  2. T. G. Elenina
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Correspondence to G. G. Elenin.

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Original Russian Text © G.G. Elenin, T.G. Elenina, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 7, pp. 950–961.

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Elenin, G.G., Elenina, T.G. Adaptive symplectic conservative numerical methods for the Kepler problem. Diff Equat 53, 923–934 (2017). https://doi.org/10.1134/S0012266117070096

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  • DOI: https://doi.org/10.1134/S0012266117070096

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