On the numerical solution of hyperbolic IBVP with high-order stable finite difference schemes

Abstract

The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The third and fourth orders of accuracy difference schemes for the approximate solution of this problem are presented. The stability estimates for the solutions of these difference schemes are established. A finite difference method and some results of numerical experiments are presented in order to support theoretical statements. MSC: 65J10, 65M12, 65N12, 35L30.