IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1105-d1077289.html
   My bibliography  Save this article

High Order Energy Preserving Composition Method for Multi-Symplectic Sine-Gordon Equation

Author

Listed:
  • Jianqiang Sun

    (Department of Mathematics, School of Science, Hainan University, Haikou 570228, China)

  • Jingxian Zhang

    (Department of Mathematics, School of Science, Hainan University, Haikou 570228, China)

  • Jiameng Kong

    (Department of Mathematics, School of Science, Hainan University, Haikou 570228, China)

Abstract

A fourth-order energy preserving composition scheme for multi-symplectic structure partial differential equations have been proposed. The accuracy and energy conservation properties of the new scheme were verified. The new scheme is applied to solve the multi-symplectic sine-Gordon equation with periodic boundary conditions and compared with the corresponding second-order average vector field scheme and the second-order Preissmann scheme. The numerical experiments show that the new scheme has fourth-order accuracy and can preserve the energy conservation properties well.

Suggested Citation

  • Jianqiang Sun & Jingxian Zhang & Jiameng Kong, 2023. "High Order Energy Preserving Composition Method for Multi-Symplectic Sine-Gordon Equation," Mathematics, MDPI, vol. 11(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1105-:d:1077289
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1105/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1105/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiang, Chaolong & Sun, Jianqiang & Li, Haochen & Wang, Yifan, 2017. "A fourth-order AVF method for the numerical integration of sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 144-158.
    Full references (including those not matched with items on IDEAS)

    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. Almushaira, Mustafa, 2023. "Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Xing, Zhiyong & Wen, Liping & Wang, Wansheng, 2021. "An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional Sine–Gordon equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 624-641.
    3. Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2021. "A Space-Time Fully Decoupled Wavelet Integral Collocation Method with High-Order Accuracy for a Class of Nonlinear Wave Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    4. Luigi Brugnano & Gianluca Frasca-Caccia & Felice Iavernaro, 2019. "Line Integral Solution of Hamiltonian PDEs," Mathematics, MDPI, vol. 7(3), pages 1-28, March.
    5. Martin-Vergara, Francisca & Rus, Francisco & Villatoro, Francisco R., 2019. "Padé numerical schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 232-243.

    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:gam:jmathe:v:11:y:2023:i:5:p:1105-:d:1077289. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.