Spectrally Accurate Energy-preserving Methods for the Numerical Solution of the "Good" Boussinesq Equation
This work provides a geometric numerical integration approach for a specific nonlinear wave equation, but the results are incremental and limited to the Boussinesq equation.
The authors developed spectrally accurate energy-preserving numerical methods for the good Boussinesq equation by combining a Hamiltonian-preserving space discretization with energy-conserving Runge-Kutta integrators, demonstrating effectiveness through numerical tests.
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.