Well-posed solvability of the boundary value problem for difference equations of elliptic type.

*(English)*Zbl 0818.65046The paper is devoted to the construction and investigation of difference schemes of high order accuracy for approximately solving the boundary value problem (*) $-{v}^{\text{'}\text{'}}\left(t\right)+Av\left(t\right)=f\left(t\right)$, $(0\le t\le 1)$, $v\left(0\right)={v}_{0}$, $v\left(1\right)={v}_{1}$, 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.

Reviewer: P.Talpalaru (Iaşi)