Ashyralyyev, Charyyar; Akyuz, Gulzipa; Cakalli, H.; Kocinac, L.D.R.; Ashyralyev, A.; Harte, R.; Dik, M.; Canak, I.; Kandemir, H.S.; Tez, M.

In this work, we discuss a third order of accuracy difference scheme for approximate solution of the elliptic overdetermined multi-point problem in the Hilbert space. Functional operator approach is used to study existence and uniqueness of solution of difference problem. Stability, almost coercive stability and coercive stability estimates for solution of difference scheme are established.

Ashyralyyev, Charyyar; Akyuz, Gulzipa

In this paper, we apply finite difference method to Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions. Stability, coercive stability inequalities for solution of the first and second order of accuracy difference schemes (ADSs) are proved. Then, established abstract results are applied to get stable difference schemes for Bitsadze-Samarskii type overdetermined elliptic multidimensional differential problems with multipoint nonlocal boundary conditions. Finally, numerical results with explanation on the realization in two dimensional and three dimensional cases are presented.

Ashyralyyev, Charyyar; Akyuz, Gulzipa; Dedeturk, Mutlu

In this work, we consider an inverse elliptic problem with Bitsadze-Samarskii type multipoint nonlocal and Neumann boundary conditions. We construct the first and second order of accuracy difference schemes (ADSs) for problem considered. We stablish stability and coercive stability estimates for solutions of these difference schemes. Also, we give numerical results for overdetermined elliptic problem with multipoint Bitsadze-Samarskii type nonlocal and Neumann boundary conditions in two and three dimensional test examples. Numerical results are carried out by MATLAB program and brief explanation on the realization of algorithm is given.