Discretizations conserving energy and other constants of the motion

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

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 language	English
Pages	17-35
Publication status	Published - 1987
Event	1st International Conference on Industrial and Applied Mathematics, ICIAM 1987 - Paris-La Vilette, France Duration: 20 Jun 1987 → 3 Jul 1987 Conference number: 1

Conference

Conference	1st International Conference on Industrial and Applied Mathematics, ICIAM 1987
Abbreviated title	ICIAM 1987
Country/Territory	France
City	Paris-La Vilette
Period	20/06/87 → 3/07/87

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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",

note = "1st International Conference on Industrial and Applied Mathematics, ICIAM 1987, ICIAM 1987 ; Conference date: 20-06-1987 Through 03-07-1987",

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T1 - Discretizations conserving energy and other constants of the motion

AU - van Beckum, F.P.H.

AU - van Groesen, E.

N1 - Conference code: 1

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

T2 - 1st International Conference on Industrial and Applied Mathematics, ICIAM 1987

Y2 - 20 June 1987 through 3 July 1987

ER -

Discretizations conserving energy and other constants of the motion

Abstract

Conference

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