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Zbl 1198.65120
Ashyralyev, Allaberen; Gercek, Okan
On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems.
(English)
[J] Abstr. Appl. Anal. 2010, Article ID 705172, 17 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

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 2000:
*65L10 Boundary value problems for ODE (numerical methods)
34G10 Linear ODE in abstract spaces
35M13
65M06 Finite difference methods (IVP of PDE)

Keywords: difference scheme; abstract nonlocal boundary value problem; Hilbert space; self-adjoint positive definite operator; well posedness; Hölder spaces; elliptic-parabolic equations; numerical example

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