Energy conservation issues in the numerical solution of the nonlinear wave equation

Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro

Published 2014-10-26Version 1

In this paper we discuss energy conservation issues related to the numerical solution of the nonlinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the specific boundary conditions at hand. We relate the conservation properties of the original problem to those of its semi-discrete version obtained by the method of lines. Subsequently, we show that the very same properties can be transferred to the solutions of the fully discretized problem, obtained by using energy-conserving methods in the HBVMs (Hamiltonian Boundary Value Methods) class.