The spectral discretization of the second-order wave equation

Abstract

In this paper we deal with the discretization of the second order wave equation by the implicit Euler scheme for the time and the spectral method for the space. We prove that the time semi discrete and the full discrete problems are well posed. We show an optimal error estimates related to both variables time and space.

Keywords

• wave equation
• implicit euler scheme
• spectral discretization
• a priori analysis
• error estimate
• primary 35q35
• secondary 65m12