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Exponentially fitted symplectic integrator.

Abstract

In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the "classical" symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.

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BibTeXRIS

T E Simos, Jesus Vigo-Aguiar. 2003-01-08. Exponentially fitted symplectic integrator.. https://doi.org/10.1103/physreve.67.016701

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