Discretizations conserving energy and other constants of the motion

F.P.H. van Beckum, E. van Groesen

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    Abstract

    Various evolution equations from mathematical physics conserve one or more integrals (constants of the motion; e.g. the energy) and have solutions in the form of steadily propagating waves (e.g. solitairy waves). In spatial discretizations these properties are generally lost. However, observing that the properties are a consequence of a certain variational structure (Poisson structL!re) of the evolution equation, we derive discretizations in such a way that they inherit this structure. Consequently the constants of the motion and the existence of steadily propagating
    waves are conserved.
    Calculations are shown for the Korteweg-de Vries equation as an example.
    Original languageEnglish
    Pages17-35
    Publication statusPublished - 1987
    Event1st International Conference on Industrial and Applied Mathematics, ICIAM 1987 - Paris-La Vilette, France
    Duration: 20 Jun 19873 Jul 1987
    Conference number: 1

    Conference

    Conference1st International Conference on Industrial and Applied Mathematics, ICIAM 1987
    Abbreviated titleICIAM 1987
    CountryFrance
    CityParis-La Vilette
    Period20/06/873/07/87

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    van Beckum, F. P. H., & van Groesen, E. (1987). Discretizations conserving energy and other constants of the motion. 17-35. Paper presented at 1st International Conference on Industrial and Applied Mathematics, ICIAM 1987, Paris-La Vilette, France.