Ashyralyyev, Charyyar; Gönenç, Ahmet; Ashyralyev, A.; Ashralyyev, C.; Erdogan, A.S.; Lukashov, A.; Sadybekov, M.

In this work, we consider approximation of nonlocal reverse parabolic problem with second kind boundary and integral conditions. Stability and coercive stability estimates for solution of difference scheme are obtained. Some illustrations of numerical results in examples of one and two dimensional reverse parabolic equations are presented.

Ashyralyev, Allaberen; Ashyralyyev, Charyyar; Zvyagin, Viktor G.; Ashyralyev, A.; Ashralyyev, C.; Erdogan, A.S.; Lukashov, A.; Sadybekov, M.

We study the well-posedness of the source identification problem for the two dimensional elliptic differential equation with nonlocal boundary conditions. Applying operator approaches, the exact estimates for the solution of this problem in Hölder norms are established.

Ashyralyyev, Charyyar; Çay, Aysel; Ashyralyev, A.; Sadybekov, M.; Lukashov, A.

The current paper is devoted to overdetermined elliptic problem with integral condition for derivatives. This overde-termined problem is converted to auxiliary nonlocal boundary value problem (ANBVP) with integral boundary condition. Well-posedness of abstract problem is established. Then, obtained results are used to obtain stability inequalities for solution of three Neumann-type inverse elliptic problems with integral condition to multidimensional differential equation.

Ashyralyyev, Charyyar; Akyüz, Gulzlpa; Ashyralyev, A.; Sadybekov, M.; Lukashov, A.

In this study, a third order of accuracy difference scheme for Bitsadze-Samarskii type multi-point elliptic overdetermined problem is studied. For solution of constructed difference problem stability, almost coercive stability and coercive stability estimates are established. The theoretical statements for the solution of this difference problem are supported by numerical results in test example by using Matlab.

Ashyralyyev, Charyyar; Öztürk, Beyza; Ashyralyev, A.; Sadybekov, M.; Lukashov, A.

In this study, we generalize the well-known finite difference method to compute derivatives of a real-valued function to approximate complex derivatives wz and wz for complex-valued function w. Exploring different combinations of terms, we derive several approximations to compute the first order derivatives of complex-valued function. The first, second, third and fourth order of accuracy finite differences to calculate derivatives are studied. Error analysis in test examples are carried out by using Matlab program.

Ashyralyyev, Charyyar; Dedeturk, Mutlu; Lukashov, A.; Ashyralyev, A.

Approximation of Dirichlet type overdetermined multidimensional elliptic problem with Dirichlet-Neumann boundary conditions are discussed. A third order of accuracy difference scheme for its approximate solution is proposed. The stability, almost coercive stability and coercive stability inequalities for the solution of constructed difference scheme are established. Test example for a two-dimensional elliptic problem is presented.

Ashyralyev, Allaberen; Cakir, Zafer; Lukashov, A.; Ashyralyev, A.

In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

Ashyralyyev, Charyyar; Akyüz, Gulzipa; Lukashov, A.; Ashyralyev, A.

In this study, we discuss well-posedness of Bitsadze-Samarskii type inverse elliptic problem with Dirichlet conditions. We establish abstract results on stability and coercive stability estimates for the solution of this inverse problem. Then, the abstract results are applied to three overdetermined problems for the multi-dimensional elliptic equation with different boundary conditions. Stability inequalities for solutions of these applications are obtained.

Ashyralyyev, Charyyar; Lukashov, A.; Ashyralyev, A.; Malkowsky, E.; Basar, F.

In the present paper, inverse elliptic problem with Neumann type overdetermination is discussed. A fourth order of accuracy difference scheme for the solution of this identification problem is presented. Stability, almost coercive stability and coercive inequalities for the solution of difference problem are obtained. In application, a fourth order approximation of the inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition is studied.