Uniform boundary stabilization for the finite difference discretization of the 1-D wave equation

摘要

In this paper, we consider a finite difference fully discretization for the 1?D wave equation with a boundary feedback and we analyze the exponential decay of the energy of solutions. First, we prove that a uniform boundary observability has a positive answer for a conservative system when the mesh size tends to zero using Fourier series technique. Then, we prove that the decay rate of the energy is uniform with respect to the mesh size. Finally, we describe some numerical experiments developed in Matlab to illustrate the results proved in this paper.