IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i17p3788-d1232296.html
   My bibliography  Save this article

Stability and Convergence Analysis of Multi-Symplectic Variational Integrator for Nonlinear Schrödinger Equation

Author

Listed:
  • Siqi Lv

    (Department of Information and Computing Science, College of Science, Jiangnan University, Wuxi 214122, China)

  • Zhihua Nie

    (Jiangxi Institute of Intelligent Industry Technology Innovation, Nanchang 330052, China)

  • Cuicui Liao

    (Department of Information and Computing Science, College of Science, Jiangnan University, Wuxi 214122, China)

Abstract

Stability and convergence analyses of the multi-symplectic variational integrator for the nonlinear Schr o ¨ dinger equation are discussed in this paper. The variational integrator is proved to be unconditionally linearly stable using the von Neumann method. A priori error bound for the scheme is given from the Sobolev inequality and the discrete conservation laws. Subsequently, the variational integrator is derived to converge at O ( Δ x 2 + Δ t 2 ) in the discrete L 2 norm using the energy method. The numerical experimental results match our theoretical derivation.

Suggested Citation

  • Siqi Lv & Zhihua Nie & Cuicui Liao, 2023. "Stability and Convergence Analysis of Multi-Symplectic Variational Integrator for Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 11(17), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3788-:d:1232296
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/17/3788/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/17/3788/
    Download Restriction: no
    ---><---

    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:17:p:3788-:d:1232296. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.