Numerical Analysis for a Class of Variational Integrators

Yihan Shen and Yajuan Sun ()
Additional contact information
Yihan Shen: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Yajuan Sun: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Mathematics, 2025, vol. 13, issue 15, 1-28

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.

Keywords: inverse variational problem; Kepler problem; modified Lagrangian; Noether’s theorem; variational integrator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/15/2326/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/15/2326/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:15:p:2326-:d:1707057

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().