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A Tenth Order Symplectic Runge–Kutta–Nyström Method

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Abstract

A tenth order explicit symmetric and in consequence symplectic Runge–Kutta–Nyström method is presented here. We derive the order conditions needed and solve them for the parameters of the method. Numerical results indicate the superiority of the new method compared to the other high order symplectic methods appeared in the literature until now.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece, e-mail

    Ch. Tsitouras

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  1. Ch. Tsitouras
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Tsitouras, C. A Tenth Order Symplectic Runge–Kutta–Nyström Method. Celestial Mechanics and Dynamical Astronomy 74, 223–230 (1999). https://doi.org/10.1023/A:1008346516048

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