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On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems. (English) Zbl 1198.65120
Summary: A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem $- d^{2}u(t)/dt^{2}+Au(t)=g(t), (0\leq t\leq 1), du(t)/dt - Au(t)=f(t), ( - 1\leq t\leq 0), u(1)=u( - 1)+\mu$ for differential equations in a Hilbert space $H$ with a self-adjoint positive definite operator $A$ is considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.

MSC:
 65L10 Boundary value problems for ODE (numerical methods) 34G10 Linear ODE in abstract spaces 35M13 Initial-boundary value problems for PDE of mixed type 65M06 Finite difference methods (IVP of PDE)
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References:
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