Local structure-preserving algorithms for the “good” Boussinesq equation

In this paper, we derive a series of local structure-preserving algorithms for the “good” Boussinesq equation, including multisymplectic geometric structure-preserving algorithms, local energy-preserving algorithms and local momentum-preserving algorithms. The outstanding advantage of the proposed a...

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Vydáno v:Journal of computational physics Ročník 239; s. 72 - 89
Hlavní autoři: Cai, Jiaxiang, Wang, Yushun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.04.2013
Témata:
Boussinesq equation
Energy
Momentum
Multisymplectic
Structure-preserving algorithm
Momentum
Energy
Structure-preserving algorithm
Boussinesq equation
Multisymplectic
ISSN:0021-9991, 1090-2716
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Popis
Shrnutí:In this paper, we derive a series of local structure-preserving algorithms for the “good” Boussinesq equation, including multisymplectic geometric structure-preserving algorithms, local energy-preserving algorithms and local momentum-preserving algorithms. The outstanding advantage of the proposed algorithms is that they conserve these local structures in any time-space region exactly. For example, the proposed local energy-preserving algorithms preserve the local energy conservation law in any local domain. Therefore, the local structure-preserving algorithms overcome the shortage of global structure-preserving algorithms on the boundary conditions. Especially, with suitable boundary conditions such as periodic or homogeneous boundary conditions, the local structure-preserving algorithms will be global structure-preserving algorithms. Numerical results verify the theoretical analysis.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.01.009