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An energy-preserving exponentially-fitted continuous stage Runge–Kutta method for Hamiltonian systems

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Abstract

Recently, the symplectic exponentially-fitted methods for Hamiltonian systems with periodic or oscillatory solutions have been attracting a lot of interest. As an alternative to them, in this paper, we propose a class of energy-preserving exponentially-fitted methods. For this aim, we show sufficient conditions for energy-preservation in terms of the coefficients of continuous stage Runge–Kutta (RK) methods, and extend the theory of exponentially-fitted RK methods in the context of continuous stage RK methods. Then by combining these two theories, we derive second and fourth order energy-preserving exponentially-fitted schemes.

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Acknowledgments

The author is thankful for various comments by the reviewers. The author is grateful to Takayasu Matsuo for his careful reading of this manuscript and helpful suggestions. The author is supported by the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists.

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  1. Graduate School of Information Science and Technology, The University of Tokyo, Hongo 7-3-1, Bunkyo- ku, Tokyo, 113-0033, Japan

    Yuto Miyatake

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  1. Yuto Miyatake
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Correspondence to Yuto Miyatake.

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Communicated by Christian Lubich.

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Miyatake, Y. An energy-preserving exponentially-fitted continuous stage Runge–Kutta method for Hamiltonian systems. Bit Numer Math 54, 777–799 (2014). https://doi.org/10.1007/s10543-014-0474-4

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