Article ID Journal Published Year Pages File Type
4626293 Applied Mathematics and Computation 2015 29 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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