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