An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation

We employ the multi-wavelet Galerkin method for the numerical solution of the telegraph equation with initial and boundary conditions. The problem becomes a sparse system of linear equations and the GMRES method is used to solve this system. The advantages of this scheme are complexity reduction, simplicity, and less grid selection. The convergence analysis is investigated and numerical experiments guarantee it. To show the ability of the method, we compare it with other methods and it can be confirmed that our results are better than others. Keywords: hyperbolic equations; Galekin method; multi-wavelet Mathematics Subject Classification: 35L20, 65M60, 65T60 1