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Zbl 1077.39015
Ashyralyev, A.; Karatay, I.; Sobolevskii, P.E.
On well-posedness of the nonlocal boundary value problem for parabolic difference equations.
(English)
[J] Discrete Dyn. Nat. Soc. 2004, No. 2, 273-286 (2004). ISSN 1026-0226; ISSN 1607-887X/e

In an arbitrary Banach space, the authors consider a nonlocal boundary value problem for the difference equation $$\frac{u_k - u_{k-1}}{\tau} + A u_k = \varphi_k, \ 1 \le k \le N, \ N\tau = 1, \ u_0 = u_{[\lambda/\tau]} + \varphi, \tag 1$$ where $A$ is a strongly positive operator. Stability and coercive stability of (1) in various Banach spaces are studied. As applications, difference schemes of boundary-value problems for parabolic equations are considered.
[Victor I. Tkachenko (Ky{\"\i}v)]
MSC 2000:
*39A12 Discrete version of topics in analysis
39A10 Difference equations
47B39 Difference operators (operator theory)
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
34G10 Linear ODE in abstract spaces

Keywords: difference equation; nonlocal boundary value problem; parabolic equation; stability; Banach space

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