New energy-preserving schemes using Hamiltonian Boundary Value and Fourier pseudospectral methods for the numerical solution of the “good” Boussinesq equation

Abstract

Two energy-preserving schemes are proposed for the “good” Boussinesq (GBq) equation using the Hamiltonian Boundary Value and Fourier pseudospectral methods. The equation is discretized in space by Fourier pseudospectral method and in time by Hamiltonian Boundary Value methods (HBVMs). The outstanding advantages of the proposed schemes are that they can precisely conserve the global mass and energy, and provide highly accurate results. The single solitary wave, the interaction of two solitary waves and the birth of solitary waves are presented to validate the accuracy and conservation properties of the proposed schemes. In addition, we also compare our numerical results with other known studied methods in terms of numerical accuracy and conservation properties.