A numerical algorithm for the solution of telegraph equations

In this paper, we present a new competitive numerical scheme to solve nonlinear telegraph equations. The method is based on Rothe’s approximation in time discretization and on the Wavelet–Galerkin in the spatial discretization. The approximate solutions converge in the space C(0,T);L2(Ω)∩L2(0,T);W01,2(Ω) to the variational solution. A full error analysis is performed and a numerical experiment is given to illustrate the good convergence behavior of the approximate solution.