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.