Numerical resolution of the wave equation using the spectral method

Abstract

Abstract We present a new procedure for the numerical study of the wave equation. We use the spectral discretization method associated with the Euler scheme for spatial and temporal discretization. A detailed numerical analysis leads to an a priori error estimate. We confirm the high precision of the method presented by a numerical study.

Keywords

• Wave equation
• Spectral method
• Backward Euler scheme
• A priori error estimate
• Implementation