New Rothe-wavelet method for solving telegraph equations

Abstract

In this article, we present a new competitive scheme to solve one of the most important cases in hyperbolic partial differential equations which is called telegraph equations. This method is based on Rothe's approximation in time discretisation and on the wavelet-Galerkin in the spatial discretisation. For comparison of wavelets, we use sin–cos, Legendre and Daubechies wavelets as basis in projection methods. For showing efficiency of method, a numerical experiment, for which the exact solution is known, is considered.

Keywords:

• hyperbolic partial differential equations
• telegraph equations
• Rothe-wavelet-Galerkin method
• error analysis