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Symplectic Exponentially-Fitted Modified Runge-Kutta Methods of the Gauss Type: Revisited

In: Recent Advances in Computational and Applied Mathematics

Author

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  • G. Vanden Berghe

    (Universiteit Gent, Vakgroep Toegepaste Wiskunde en Informatica)

  • M. Van Daele

    (Universiteit Gent, Vakgroep Toegepaste Wiskunde en Informatica)

Abstract

The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators are constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (Exponential Fitting, Kluwer Academic, Dordrecht, 2004). Numerical experiments for some oscillatory problems are presented and compared to the results obtained by previous methods.

Suggested Citation

  • G. Vanden Berghe & M. Van Daele, 2011. "Symplectic Exponentially-Fitted Modified Runge-Kutta Methods of the Gauss Type: Revisited," Springer Books, in: Theodore E. Simos (ed.), Recent Advances in Computational and Applied Mathematics, chapter 0, pages 289-306, Springer.
    • Handle: RePEc:spr:sprchp:978-90-481-9981-5_13
    DOI: 10.1007/978-90-481-9981-5_13
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