Ashyralyyev, Charyyar

In this study, a source identification problem for elliptic differential equation with integral type non-local condition is discussed. The second order of accuracy difference scheme for elliptic non-local source identification problem is studied. Using spectral resolution of a self-adjoint operator, stability and coercive stability estimates for solution of difference scheme are established. Subsequently, difference scheme for an approximate solution of multi-dimensional boundary-value problem with integral type non-local and first kind boundary conditions is investigated for stability. Numerical results for 2D and 3D examples are illustrated.

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

In this work, we study time-nonlocal boundary value problem for multi-dimensional parabolic partial differential equation. Two difference schemes for approximate solution of non-local boundary value problem are discussed. Theorems on stability of solutions both difference schemes are given without proof. Numerical results for test examples are outlined.

Ashyralyev, Allaberen; Al-Hammouri, Ahmad; Ashyralyyev, Charyyar

The present paper is devoted to study the first order of accuracy absolute stable difference scheme for the approximate solution of the space identification problem for the elliptic-telegraph equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the difference scheme is established. In applications, theorems on the stability of difference schemes for two types of the space identification problems for multidimensional elliptic-telegraph partial differential equations are proved. Numerical analysis is provided.

Ashyralyyev, Charyyar; G¨onenc¸, Ahmet

In this paper, we study Crank-Nicholson difference scheme for approximate solutions of parabolic nonlocal reverse problem with integral and Neumann boundary conditions. Stability estimates for its solution are established. Via Mathlab framework, we give numerical example with explanation on computer realization.

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.

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; Ashyralyev, A.; Kalmenov, T.S.; Ruzhansky, M.V.; Sadybekov, M.A.; Suragan, D.

In the present paper, identification elliptic problem in a Hilbert space with Dirichlet and integral boundary conditions is discussed. Identification problem is reduced to auxiliary nonlocal boundary value problem with nonlocal integral condition. Operator approach is used to prove stability and coercive stability inequalities for solution of source identification elliptic problem in the case of a self-adjoint positive definite operator in a differential equation. As applications, four mixed boundary value problems for strongly elliptic multidimensional partial differential equation are investigated. Theorems on stability of solutions of these boundary value problems are established.

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

In this study, the first order of accuracy difference scheme for approximate solution of source identification elliptic problem with integral and second kind boundary conditions is considered. Stability and coercive stability estimates for solution of the difference scheme are described. Moreover, test example with computation results is given.

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

Finite difference method to solve nonlocal reverse parabolic (RP) problem with integral condition are applied. The second order of accuracy difference scheme (ADS) for approximation of RP problem is proposed. Stability estimates (SEs) for solutions of this difference scheme (DS) are proved. Later, we propose the second order of ADS for approximation of multidimensional RP boundary value problem (BVP) with first kind boundary condition (BC) and establish SEs for its solu-tion. Numerical illustration for simple test problems is given.

Ashyralyyev, Charyyar; Akkan, Pinar

We study a source identification problem for a parabolic equation with multipoint nonlocal boundary condition. Stability estimates for the solution of abstract source identification problem are established. In application, stability estimates for the solution of the overdetermined mixed boundary value problem for multidimensional parabolic equation are obtained. The first and second order of accuracy difference schemes for the approximate solution of this problem are constructed. Stability estimates for solutions of these difference schemes are proved. Numerical illustration for a simple test problem is presented.

Ashyralyyev, Charyyar

In this paper, we study the approximation of reverse parabolic problem with integral boundary condition. The Rothe difference scheme for an approximate solution of reverse problem is discussed. We establish stability and coercive stability estimates for the solution of the Rothe difference scheme. In sequel, we investigate the first order of accuracy difference scheme for approximation of boundary value problem for multidimensional reverse parabolic equation and obtain stability estimates for its solution. Finally, we give numerical results together with an explanation on the realization in one- and two-dimensional test examples.

Ashyralyev, Allaberen; Ashyralyyev, Charyyar; Cakalli, H.; Kocinac, L.D.R.; Harte, R.; Cavalcanti, V.N.D.; Ashyralyev, A.; Sakalli, I.; Canak, I.; Gurtug, O.

Ashyralyyev, Charyyar; Karabey, Suzan; Cakalli, H.; Kocinac, L.D.R.; Harte, R.; Cavalcanti, V.N.D.; Ashyralyev, A.; Sakalli, I.; Canak, I.; Gurtug, O.

In the present paper, Neumann type elliptic overdetermined multipoint boundary value problem is discussed. The first and second order of accuracy difference schemes (ADSs) for the numerical solution of elliptic overdetermined multipoint boundary value problems are presented. Stability estimates for solutions of difference schemes are obtained. Numerical results for mixed boundary value problem are given.

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; 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; 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

In this paper, we consider an inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for an inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with descriptions of numeric realization in a two-dimensional case.

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.