Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation | Zendy

Brugnano Luigi | Zendy; Gurioli Gianmarco | Zendy; Zhang Chengjian | Zendy

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Spectrally accurate energy‐preserving methods for the numerical solution of the “good” Boussinesq equation

Author(s) -

Brugnano Luigi,

Gurioli Gianmarco,

Zhang Chengjian

Publication year - 2019

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.22353

Subject(s) - discretization , mathematics , runge–kutta methods , boundary value problem , boussinesq approximation (buoyancy) , mathematical analysis , numerical analysis , hamiltonian (control theory) , energy method , boundary values , mathematical optimization , physics , mechanics , convection , natural convection , rayleigh number

In this paper we study the geometric numerical solution of the so called “good” Boussinesq equation. This goal is achieved by using a convenient space semi‐discretization, able to preserve the corresponding Hamiltonian structure, then using energy‐conserving Runge–Kutta methods in the Hamiltonian boundary value method class for the time integration. Numerical tests are reported, confirming the effectiveness of the proposed method.

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