Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the "Good" Boussinesq Equation

Abstract: In this paper we study the geometric 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.