Stability of a second order of accuracy difference scheme for hyperbolic equation in a Hilbert space

Abstract

The initial-value problem for hyperbolic equation d(2)u(t)/dt(2) + A(t) u(t) = f (t) (0 <= t <= T), u(0) =phi, u' (0) = psi in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established. Copyright (c) 2007 A. Ashyralyev and M. E. Koksal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.