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Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods

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Abstract

In this work, we give the general framework for constructing trigonometrically fitted symplectic Runge–Kutta–Nyström (RKN) methods from symplectic trigonometrically fitted partitioned Runge–Kutta (PRK) methods. We construct RKN methods from PRK methods with up to five stages and fourth algebraic order. Numerical results are given for the two-body problem and the perturbed two-body problem.

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Authors and Affiliations

  1. Department of International Trade, Technological Educational, Institute of Western Macedonia at Kastoria, P.O. Box 30, 521 00, Kastoria, Greece

    T. Monovasilis

  2. Department of Computer Science and Technology, Technological Educational Institution of Western Macedonia at Kastoria, Kastoria, Greece

    Z. Kalogiratou

  3. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    T. E. Simos

  4. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, Tripolis, GR-221 00, Greece

    T. E. Simos

Authors
  1. T. Monovasilis
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  2. Z. Kalogiratou
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  3. T. E. Simos
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Correspondence to T. E. Simos.

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Active member of the European Academy of Sciences and Arts.

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Monovasilis, T., Kalogiratou, Z. & Simos, T.E. Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods. Mediterr. J. Math. 13, 2271–2285 (2016). https://doi.org/10.1007/s00009-015-0587-2

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  • DOI: https://doi.org/10.1007/s00009-015-0587-2

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