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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 3, Pages 213–226
DOI: https://doi.org/10.1070/RD2004v009n03ABEH000277
(Mi rcd743)
 

This article is cited in 34 scientific papers (total in 34 papers)

Effective computations in modern dynamics

Geometric integration via multi-space

P. Kim, P. J. Olver

Department of Mathematics, University of Minnesota, MN 55455, USA
Citations (34)
Abstract: We outline a general construction of symmetry-preserving numerical schemes for ordinary differential equations. The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis. We explain how to invariantize standard numerical integrators such as the Euler and Runge–Kutta schemes; in favorable situations, the resulting symmetry-preserving geometric integrators offer significant advantages.
Received: 20.08.2004
Bibliographic databases:
Document Type: Article
Language: English
Citation: P. Kim, P. J. Olver, “Geometric integration via multi-space”, Regul. Chaotic Dyn., 9:3 (2004), 213–226
Citation in format AMSBIB
\Bibitem{KimOlv04}
\by P.~Kim, P.~J.~Olver
\paper Geometric integration via multi-space
\jour Regul. Chaotic Dyn.
\yr 2004
\vol 9
\issue 3
\pages 213--226
\mathnet{http://mi.mathnet.ru/rcd743}
\crossref{https://doi.org/10.1070/RD2004v009n03ABEH000277}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2104169}
\zmath{https://zbmath.org/?q=an:1068.65092}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..213K}
Linking options:
  • https://www.mathnet.ru/eng/rcd743
  • https://www.mathnet.ru/eng/rcd/v9/i3/p213
  • This publication is cited in the following 34 articles:
    1. Lewis C. White, Peter E. Hydon, “Moving Frames: Difference and Differential-Difference Lagrangians”, SIGMA, 20 (2024), 006, 29 pp.  mathnet  crossref
    2. Bihlo A., Jackaman J., Valiquette F., “Invariant Variational Schemes For Ordinary Differential Equations”, Stud. Appl. Math., 148:3 (2022), 991–1020  crossref  mathscinet  isi  scopus
    3. Evgeniy I. Kaptsov, Vladimir A. Dorodnitsyn, Sergey V. Meleshko, “Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates”, Stud Appl Math, 149:3 (2022), 729  crossref
    4. Cem Gormezano, Jean-Christophe Nave, Andy T.S. Wan, “Conservative integrators for vortex blob methods on the plane”, Journal of Computational Physics, 469 (2022), 111357  crossref
    5. Dorodnitsyn V.A., Kaptsov I E., “Shallow Water Equations in Lagrangian Coordinates: Symmetries, Conservation Laws and Its Preservation in Difference Models”, Commun. Nonlinear Sci. Numer. Simul., 89 (2020), 105343  crossref  mathscinet  zmath  isi  scopus
    6. Bihlo A., Valiquette F., “Symmetry-Preserving Finite Element Schemes: An Introductory Investigation”, SIAM J. Sci. Comput., 41:5 (2019), A3300–A3325  crossref  mathscinet  zmath  isi  scopus
    7. E L Mansfield, A Rojo-Echeburúa, P E Hydon, L Peng, “Moving frames and Noether's finite difference conservation laws I”, Transactions of Mathematics and Its Applications, 3:1 (2019)  crossref
    8. Peter J. Olver, Francis Valiquette, “Recursive Moving Frames for Lie Pseudo-Groups”, Results Math, 73:2 (2018)  crossref
    9. Robert Thompson, Francis Valiquette, “Group foliation of finite difference equations”, Communications in Nonlinear Science and Numerical Simulation, 59 (2018), 235  crossref
    10. Gloria Marí Beffa, Elizabeth L. Mansfield, “Discrete Moving Frames on Lattice Varieties and Lattice-Based Multispaces”, Found Comput Math, 18:1 (2018), 181  crossref
    11. Alexander Bihlo, Francis Valiquette, Symmetries and Integrability of Difference Equations, 2017, 261  crossref
    12. Svyatoslav I. Solodushkin, Irina F. Yumanova, Rob H. De Staelen, “A difference scheme for multidimensional transfer equations with time delay”, Journal of Computational and Applied Mathematics, 318 (2017), 580  crossref
    13. Joseph Benson, Francis Valiquette, “Symmetry reduction of ordinary finite difference equations using moving frames”, J. Phys. A: Math. Theor., 50:19 (2017), 195201  crossref
    14. B. Miro, D. Rose, F. Valiquette, “Equivalence of one-dimensional second-order linear finite difference operators”, Journal of Difference Equations and Applications, 22:10 (2016), 1524  crossref
    15. Andy T.S. Wan, Alexander Bihlo, Jean-Christophe Nave, “The Multiplier Method to Construct Conservative Finite Difference Schemes for Ordinary and Partial Differential Equations”, SIAM J. Numer. Anal., 54:1 (2016), 86  crossref
    16. D Levi, L Martina, P Winternitz, “Lie-point symmetries of the discrete Liouville equation”, J. Phys. A: Math. Theor., 48:2 (2015), 025204  crossref
    17. I. A. Kogan, P. J. Olver, “Invariants of objects and their images under surjective maps”, Lobachevskii J Math, 36:3 (2015), 260  crossref
    18. Raphaël Rebelo, Francis Valiquette, “Invariant discretization of partial differential equations admitting infinite-dimensional symmetry groups”, Journal of Difference Equations and Applications, 21:4 (2015), 285  crossref
    19. Svyatoslav I. Solodushkin, Irina F. Yumanova, Rob H. De Staelen, “First order partial differential equations with time delay and retardation of a state variable”, Journal of Computational and Applied Mathematics, 289 (2015), 322  crossref
    20. Alexander Bihlo, Xavier Coiteux-Roy, Pavel Winternitz, “The Korteweg–de Vries equation and its symmetry-preserving discretization”, J. Phys. A: Math. Theor., 48:5 (2015), 055201  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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