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 HBVM class for the time integration. Numerical tests are reported, confirming the effectiveness of the proposed method.
Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the “Good” Boussinesq Equation / Luigi Brugnano, Gianmarco Gurioli, Chengjian Zhang. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - STAMPA. - 35:(2019), pp. 1343-1362. [10.1002/num.22353]
Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the “Good” Boussinesq Equation
Luigi Brugnano
;Gianmarco Gurioli;
2019
Abstract
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 HBVM class for the time integration. Numerical tests are reported, confirming the effectiveness of the proposed method.
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