IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i15p2326-d1707057.html
   My bibliography  Save this article

Numerical Analysis for a Class of Variational Integrators

Author

Listed:
  • Yihan Shen

    (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
    These authors contributed equally to this work.)

  • Yajuan Sun

    (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
    These authors contributed equally to this work.)

Abstract

In this paper, we study a geometric framework for second-order differential systems arising in classical and relativistic mechanics. For this class of systems, we derive necessary and sufficient conditions for their Lagrangian description. The main objectives of this work are to construct efficient structure-preserving variational integrators in a variational framework. To achieve this, we develop new variational integrators through Lagrangian splitting and prove their equivalence to composition methods. We display the superiority of the newly derived numerical methods for the Kepler problem and provide rigorous error estimates by analysing the Laplace–Runge–Lenz vector. The framework provides tools applicable to geometric numerical integration of both ordinary and partial differential equations.

Suggested Citation

  • Yihan Shen & Yajuan Sun, 2025. "Numerical Analysis for a Class of Variational Integrators," Mathematics, MDPI, vol. 13(15), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2326-:d:1707057
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/15/2326/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/15/2326/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:13:y:2025:i:15:p:2326-:d:1707057. 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.