Abstract
The stable difference schemes approximately solving the nonlocal boundary value problem for hyperbolic-parabolic equation d 2 u ( t ) d t 2 + A u ( t ) = f ( t ) , 0 ≤ t ≤ 1 , u ( − 1 ) = α u ( μ ) + β u ′ ( λ ) + ϕ d u ( t ) d t + A u ( t ) = g ( t ) , − 1 ≤ t ≤ 0 , | α | , | β | ≤ 1 , 0 < μ , λ ≤ 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.
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