On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations

The nonlocal boundary value problems for semilinear hyperbolic-parabolic eq uations {d(2)u(t)/dt(2) + Au (t) = f (t, u (t)) (0 less than or equal to t less than or equal to 1), du (t)/dt + Au (t) = g (t, u (t)) (- 1 less than or equal to t less than or equal to 0), u(-1) = alphau(mu) + phi, 0 less th an or equal to alpha less than or equal to 1, 0 < mu less than or equal to 1, in a Hilbert space are considered. The first and second order accuracy d ifference schemes approximately solving these problems are studied. The con vergence estimates for the solution of these difference schemes are obtaine d.