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High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods

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  • Tang, Wensheng
  • Sun, Yajuan
  • Zhang, Jingjing

Abstract

On the basis of the previous work by Tang and Zhang [37], in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.

Suggested Citation

  • Tang, Wensheng & Sun, Yajuan & Zhang, Jingjing, 2019. "High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 670-679.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:670-679
    DOI: 10.1016/j.amc.2019.06.031
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    References listed on IDEAS

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    1. Tang, Wensheng & Lang, Guangming & Luo, Xuqiong, 2016. "Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 279-287.
    2. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.
    3. Tang, Wensheng, 2018. "A note on continuous-stage Runge–Kutta methods," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 231-241.
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    Cited by:

    1. Liu, Changying & Li, Jiayin & Yang, Zhenqi & Tang, Yumeng & Liu, Kai, 2023. "Two high-order energy-preserving and symmetric Gauss collocation integrators for solving the hyperbolic Hamiltonian systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 19-32.
    2. Amodio, Pierluigi & Brugnano, Luigi & Iavernaro, Felice, 2019. "A note on the continuous-stage Runge–Kutta(–Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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