IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp670-679.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304965
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.06.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tang, Wensheng, 2018. "A note on continuous-stage Runge–Kutta methods," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 231-241.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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, 2018. "A note on continuous-stage Runge–Kutta methods," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 231-241.
    3. Jun Zhang & Jingjing Zhang & Shangyou Zhang, 2023. "Explicit Symplectic Runge–Kutta–Nyström Methods Based on Roots of Shifted Legendre Polynomial," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    4. Zhang, Jingjing, 2020. "An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. 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.
    6. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:670-679. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.