On Difference Schemes for Hyperbolic-Parabolic Equations
نویسندگان
چکیده
The nonlocal boundary value problem for a hyperbolic-parabolic equation in a Hilbert space H is considered. The difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. In applications, 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 hyperbolicparabolic equation are supported by the results of numerical experiments. 1 The differential problem Methods for numerical solutions of the nonlocal boundary value problems for hyperbolic-parabolic equations d2u(t) dt2 +Au(t) = f(t) (0 ≤ t ≤ 1), du(t) dt +Au(t) = g(t) (−1 ≤ t ≤ 0), u(−1) = αu(μ) + φ, |α| ≤ 1, 0 < μ ≤ 1, for differential equations in a Hilbert space H, with the self-adjoint positive definite operator A have been studied extensively (see [7]—[17] and the references therein).
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