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Zbl 0818.65046
Ashyralyev, Allaberen
(Ashyralev, A.)
Well-posed solvability of the boundary value problem for difference equations of elliptic type. (English)
[J] Nonlinear Anal., Theory Methods Appl. 24, No.2, 251-256 (1995). ISSN 0362-546X

The paper is devoted to the construction and investigation of difference schemes of high order accuracy for approximately solving the boundary value problem (*) $-v''(t) + A v(t) = f(t)$, $(0 \leq t \leq 1)$, $v(0) = v\sb 0$, $v(1) = v\sb 1$, in an arbitrary Banach space, where $A$ is an unbounded strongly positive operator.\par The author investigates the solvability of two steps of the difference schemes for approximately solving the abstract boundary value problem (*) reproduced by Taylor's expansion in three points. The study is based upon stability and coercive stability of this difference scheme.
[P.Talpalaru (Iaşi)]

MSC 2000:: *65J10 Equations with linear operators (numerical methods)
65L10 Boundary value problems for ODE (numerical methods)
65L12 Finite difference methods for ODE
34G10 Linear ODE in abstract spaces

Keywords: difference schemes; boundary value problem; Banach space; coercive stability

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Zentralblatt MATH Berlin [Germany]