NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM FOR THE HYPERBOLIC EQUATION WITH INITIAL JUMP

In this paper we consider the initial-boundary value problem for a second orderhyperbolic equation with initial jump.The bounds on the derivatives of the exact solutionare given.Then a difference scheme is constructed on a non-uniform grid.Finally,uniformconvergence of the difference solution is proved in the sense of the discrete energy norm.