Stability of difference schemes for hyperbolic-parabolic equations

Abstract

The stable difference schemes approximately solving the nonlocal boundary value problem for hyperbolic-parabolic equation d(2)u(t)/dt(2) + Au(t) = f(t), 0 <= t <= 1, u(-1) = alpha u(mu) + beta u'(lambda) + phi, du(t)/dt + Au(t) = g(t), -1 <= t <= 0, vertical bar alpha vertical bar,vertical bar beta vertical bar <= 1, 0 < mu, lambda <= 1, in a Hilbert space H with self-adjoint positive definite operator A are presented. The stability estimates for the solutions of the difference schemes of the mixed type boundary value problems for hyperbolic-parabolic equations are obtained. The theoretical statements for the solution of these difference schemes for hyperbolic-parabolic equation are supported by the results of numerical experiments. (c) 2005 Elsevier Ltd. All rights reserved.