Stability of difference schemes for hyperbolic-parabolic equations

The stable difference schemes approximately solving the nonlocal boundary value problem for hyperbolic-parabolic equation 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.