Stability of difference schemes for hyperbolic-parabolic equations

The stable difference schemes approximately solving the nonlocal boundary value problem for hyperbolic-parabolic equationd2u(t)dt2+Au(t)=f(t),0≤t≤1,u(−1)=αu(μ)+βu′(λ)+ϕdu(t)dt+Au(t)=g(t),−1≤t≤0,|α|,|β|≤1,0<μ,λ≤1in 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.