Yazarlar
- Ashyralyyev, Charyyar(12)
- Dedeturk, Mutlu(4)
- Ashyralyev, A.(3)
- Akay, K.U.(2)
- Akyuz, Gulzipa(2)
- Ashyralyev, A(2)
- Ashyralyyev, C.(2)
- Cakalli, H.(2)
- Canak, I.(2)
- Gurtug, O.(2)
- Harte, R.(2)
- Kandemir, H.S.(2)
- Kocinac, L.D.R.(2)
- Malkowsky, E(2)
- Sahin, H.(2)
- Tez, M.(2)
- Ucgun, F.C.(2)
- Uyaver, S.(2)
- Akkan, Yasar(1)
- Akyel, T.(1)
- Basar, F.(1)
- Cavalcanti, M.M.(1)
- Cavalcanti, V.N.D.(1)
- Cay, A.(1)
- Dik, M.(1)
- Gul, I.(1)
- Karabey, Suzan(1)
- Lukashov, A.(1)
- Malkowsky, E.(1)
- Onvural, O.R.(1)
- Sakalli, I.(1)
- Savas, E.(1)
- Sezer, S.A.(1)
- Turkoglu, A.D.(1)
- Turkoglu, D.(1)
- Yilmazturk, T.E.(1)
Yayınlar
- BildiriAçık Erişim2021Solution of Inverse Problem for an Elliptic Equation by Differential Transform Method
Dedeturk, Mutlu; Cakalli, H.; Kocinac, L.D.R.; Ashyralyev, A.; Harte, R.; Dik, M.; Canak, I.; Kandemir, H.S.; Tez, M.; Gurtug, O.
In this work, inverse problem for an elliptic equation is studied. We gave a numerical solution of inverse elliptic problem by differential transform method in test example.
- MakaleAçık Erişim2020Numerical solution to elliptic inverse problem with Neumann-type integral condition and overdetermination; [Интегралдық шарты бар және қайта анықталған Нейман типтi эллипстiк керi есептiң сандық есептеуi]; [Численное решение эллиптической обратной задачи с интегральным условием и переопределением типа Неймана]
Ashyralyyev, C.; Cay, A.
In modeling various real processes, an important role is played by methods of solution source identification problem for partial differential equation. The current paper is devoted to approximate of elliptic over determined problem with integral condition for derivatives. In the beginning, inverse problem is reduced to some auxiliary nonlocal boundary value problem with integral boundary condition for derivatives. The parameter of equation is defined after solving that auxiliary nonlocal problem. The second order of accuracy difference scheme for approximately solving abstract elliptic overdetermined problem is proposed. By using operator approach existence of solution difference problem is proved. For solution of constructed difference scheme stability and coercive stability estimates are established. Later, obtained abstract results are applied to get stability estimates for solution Neumann-type overdetermined elliptic multidimensional difference problems with integral conditions. Finally, by using MATLAB program, we present numerical results for two dimensional and three dimensional test examples with short explanation on realization on computer.
- BildiriAçık Erişim2019Numerical solution of Neumann type elliptic overdetermined multipoint mixed boundary value problem
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.
- MakaleYayıncıda açık erişim2018Finite difference method for bitsadze-samarskii type overdetermined elliptic problem with dirichlet conditions
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.
- MakaleAçık Erişim2017A fourth order approximation of the neumann type overdetermined elliptic problem
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.
- MakaleYalnız künye2017Approximate solution for an inverse problem of multidimensional elliptic equation with multipoint nonlocal and neumann boundary conditions
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.
- MakaleAçık Erişim2017Numerical solution to Bitsadze-Samarskii type elliptic overdetermined multipoint NBVP
Ashyralyyev, Charyyar
This paper is devoted to a Bitsadze-Samarskii type overdetermined multipoint nonlocal boundary value problem (NBVP). This inverse problem is reduced to an auxiliary multipoint NBVP. Stability estimates for the solution of the auxiliary NBVP are established. The finite difference method is applied to get the first and second order of accuracy of approximate solutions of the abstract overdetermined problem. Stability estimates for the solution of difference problems are proved. Then the established abstract results are applied to get stability estimates for the solution of the Bitsadze-Samarskii type overdetermined elliptic multidimensional differential and difference problems with multipoint nonlocal boundary conditions (NBVC). Finally, numerical results with explanation on the realization for two dimensional and three dimensional elliptic overdetermined multipoint NBVPs in test examples are presented.
- MakaleYalnız künye2015Numerical solution to inverse elliptic problem with neumann type overdetermination and mixed boundary conditions
Ashyralyyev, Charyyar; Akkan, Yasar
This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
- MakaleAçık Erişim2015Approximation of the inverse elliptic problem with mixed boundary value conditions and overdetermination
Ashyralyyev, Charyyar; Dedeturk, Mutlu
In the present study, the inverse problem for a multidimensional elliptic equation with mixed boundary conditions and overdetermination is considered. The first and second orders of accuracy in t and the second order of accuracy in space variables for the approximate solution of this inverse problem are constructed. Stability, almost coercive stability, and coercive stability estimates for the solution of these difference schemes are established. For the two-dimensional inverse problems with mixed boundary value conditions, numerical results are presented in test examples.
- BildiriYalnız künye2015Well-posedness of a fourth order of accuracy difference scheme for the Neumann type overdetermined elliptic problem
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.
- MakaleAçık Erişim2014High order of accuracy difference schemes for the inverse elliptic problem with Dirichlet condition
Ashyralyyev, Charyyar
The overdetermination problem for elliptic differential equation with Dirichlet boundary condition is considered. The third and fourth orders of accuracy stable difference schemes for the solution of this inverse problem are presented. Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established. As a result of the application of established abstract theorems, we get well-posedness of high order difference schemes of the inverse problem for a multidimensional elliptic equation. The theoretical statements are supported by a numerical example.
- MakaleAçık Erişim2014High order approximation of the inverse elliptic problem with dirichlet-neumann conditions
Ashyralyyev, Charyyar
Inverse problem for the multidimensional elliptic equation with Dirichlet-Neumann conditions is considered. High order of accuracy difference schemes for the solution of inverse problem are presented. Stability, almost coercive stability and coercive stability estimates of the third and fourth orders of accuracy difference schemes for this problem are obtained. Numerical results in a two dimensional case are given.
- BildiriYalnız künye2014Approximation of the inverse elliptic problem with mixed boundary value conditions
Ashyralyyev, Charyyar; Dedeturk, Mutlu; Ashyralyev, A; Malkowsky, E
The inverse problem for the multidimensional elliptic equation with Neumann-Dirichlet conditions are presented. For the approximate solution of this inverse problem the first and second order of accuracy in t and in space variables difference schemes are constructed. The stability, almost coercive stability and coercive stability estimates for the solution of these difference schemes are obtained. The algorithm for approximate solution is tested in a two-dimensional inverse problem.
- BildiriYalnız künye2014Inverse Neumann problem for an equation of elliptic type
Ashyralyyev, Charyyar; Ashyralyev, A; Malkowsky, E
Inverse problem for an elliptic differential equation with Neumann conditions is considered. Stability and coercive stability estimates for the solution of inverse problem with the overdetermination are obtained. The first and second order of accuracy difference schemes are presented. Stability and coercive stability inequalities for these difference schemes are given. In application, inverse problem for the multidimensional elliptic equation is studied. The first and second order of accuracy difference schemes for the multidimensional inverse problem are presented. Well-posedness of both difference problems are established. The results are supported by a numerical example for the two-dimensional elliptic equation.