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A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations. (English) Zbl 1065.35021

The authors consider the nonlocal boundary-value problem for hyperbolic equations

d 2 u(t) dt 2 +Au(t)=f(t)(0tl),u(0)=αu(1)+ϕ,u ' (0)=β ' u ' (1)+ψ

in a Hilbert space H with self-adjoint positive definite operator A. The stability estimates are obtained. The first and second order difference schemes generated by the integer power of A for approximately solving this nonlocal boundary-value are presented. The stability estimates for the difference schemes are obtained. The theoretical statements for the solution of these difference schemes are illustrated by numerical example.

MSC:
35A35Theoretical approximation to solutions of PDE
65N12Stability and convergence of numerical methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35L20Second order hyperbolic equations, boundary value problems
34G10Linear ODE in abstract spaces
35L90Abstract hyperbolic equations