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Well-posed solvability of the boundary value problem for difference equations of elliptic type. (English) Zbl 0818.65046
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. 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.

65J10Equations with linear operators (numerical methods)
65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)
34G10Linear ODE in abstract spaces
Full Text: DOI
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