On the second order of accuracy difference scheme for hyperbolic equations in a Hilbert space

Abstract

The initial-value problem for hyperbolic equation [GRAPHICS] in a Hilbert space H with the self-adjoint positive definite operators A ( t ) is considered. The second order of accuracy absolute stable difference scheme for approximately solving this abstract initial-value problem is presented. The stability estimates for the solution of this difference scheme and for the first- and second-order difference derivatives are established.