Full discretization to an hyperbolic equation with nonlocal coefficient

Abstract

We present full discretization of the telegraph equation with nonlocal coeffecient using Rothe-nite element method. For solving the equation numerically we use the Newton Raphson method, but the nonlocal term causes diffeculties because the Jacobien matrix is full. To remedy these diffeculties we apply the technique used by Sudhakar [4]. The optimal a priori error estimates for both semi discrete and fully discrete schemes are derived in V and H1 and a numerical experiment is described to support our theoretical result.