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

L. Brugnano, G. Frasca Caccia and F. Iavernaro

Applied Mathematics and Computation, 2015, vol. 270, issue C, 842-870

Abstract: In this paper we discuss energy conservation issues related to the numerical solution of the semilinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the prescribed boundary conditions. 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. Similar arguments hold true for different types of Hamiltonian partial differential equations, e.g., the nonlinear Schrödinger equation.

Keywords: Semilinear wave equation; Hamiltonian PDEs; Energy-conserving methods; Hamiltonian Boundary Value Methods; HBVMs (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:842-870

DOI: 10.1016/j.amc.2015.08.078

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