Full Discretization to an Hyperbolic Equation with Nonlocal Coefficient

We present full discretization of the telegraph equation with nonlocal coefficient using Rothe- finite element method. For solving the equation numerically we use the Newton Raphson method, but the nonlocal term causes difficulties because the Jacobien matrix is full. To remedy these difficulties 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 , introduced in (1.4), and H1() and a numerical experiment is described to support our theoretical result.