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Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage

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  • Tang, Wensheng
  • Lang, Guangming
  • Luo, Xuqiong

Abstract

Hamiltonian systems, as one of the most important class of dynamical systems, are associated with a well-known geometric structure called symplecticity. Symplectic numerical algorithms, which preserve such a structure are therefore of interest. In this article, we study the construction of symplectic (partitioned) Runge–Kutta methods with continuous stage. This construction of symplectic methods mainly relies upon the expansion of orthogonal polynomials and the simplifying assumptions for (partitioned) Runge–Kutta type methods. By using suitable quadrature formulae, it also provides a new and simple way to construct symplectic (partitioned) Runge–Kutta methods in classical sense.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:279-287
    DOI: 10.1016/j.amc.2016.04.026
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    Cited by:

    1. Tang, Wensheng & Zhang, Jingjing, 2019. "Symmetric integrators based on continuous-stage Runge–Kutta–Nyström methods for reversible systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 1-12.
    2. 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.
    3. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.
    4. 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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