Discretizations conserving energy and other constants of the motion

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

    Research output: Contribution to conferencePaper

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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

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    title = "Discretizations conserving energy and other constants of the motion",
    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 propagatingwaves are conserved.Calculations are shown for the Korteweg-de Vries equation as an example.",
    author = "{van Beckum}, F.P.H. and {van Groesen}, E.",
    year = "1987",
    language = "English",
    pages = "17--35",

    }

    Discretizations conserving energy and other constants of the motion. / van Beckum, F.P.H.; van Groesen, E.

    1987. 17-35.

    Research output: Contribution to conferencePaper

    TY - CONF

    T1 - Discretizations conserving energy and other constants of the motion

    AU - van Beckum, F.P.H.

    AU - van Groesen, E.

    PY - 1987

    Y1 - 1987

    N2 - 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 propagatingwaves are conserved.Calculations are shown for the Korteweg-de Vries equation as an example.

    AB - 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 propagatingwaves are conserved.Calculations are shown for the Korteweg-de Vries equation as an example.

    M3 - Paper

    SP - 17

    EP - 35

    ER -