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- MakaleAçık Erişim2021On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem
Ashyralyyev, C.; Akyuz, G.
In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi point overdetermined boundary value problem for multidimensional elliptic partial differential equations.
AtıfOpenAlex1
İncele - MakaleAçık Erişim2021On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem; [Көпнүктелi қайтаанықталған эллипстiк есеп үшiн төртiншi реттi дәлдiктi тұрақтылық айырымдық схемасы туралы]; [Об устойчивой разностной схеме четвертого порядка точности для многоточечной переопределенной эллиптической задачи]
Ashyralyyev, C.; Akyuz, G.
In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multipoint overdetermined boundary value problem for multidimensional elliptic partial differential equations.
AtıfOpenAlex5
İncele - MakaleAçık Erişim2020A note on well-posedness of source identification elliptic problem in a Banach space; [Банах кеңiстiгiнде дереккөздi сәйкестендiруде эллипстiк есептiң корректiлiгi туралы ескерту]; [Замечание о корректности эллиптической задачи идентификации источника в банаховом пространстве]
Ashyralyev, A.; Ashyralyyev, C.; Zvyagin, V.G.
We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in Hölder norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained.
AtıfOpenAlex1İncele - 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.
AtıfScopus7WoS6OpenAlex9İncele - MakaleYayıncıda açık erişim2018Scopus SJRQ2Finite 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.
AtıfScopus10WoS7OpenAlex11İncele - MakaleAçık Erişim2017Scopus SJRQ3A 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.
AtıfScopus19WoS12OpenAlex17İncele - MakaleYalnız künye2017Scopus SJRQ2Stability Estimates for Solution of Neumann-Type Overdetermined Elliptic Problem
Ashyralyyev, Charyyar
This paper addresses estimation of the solution of inverse problem for the elliptic type equation with second kind boundary conditions and Neumann-type overdetermination at the interior point. We prove various estimates for the solution of this identification problem. Then, the first order accuracy stable difference scheme is studied. The stability, almost coercive stability, and coercive stability inequalities for its solution are obtained. The theoretical results can be applied to investigate identification problems for multidimensional elliptic equation with different kind of boundary conditions.
AtıfScopus28WoS18OpenAlex26İncele - BildiriYalnız künye2016A third order of accuracy difference scheme for Dirichlet type overdermined problem with mixed boundary value conditions
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.
- BildiriYalnız künye2016Stability estimates for solution of IBVP to fractional parabolic differential and difference equations
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.
- BildiriYalnız künye2016Stability estimates for solution of Bitsadze-Samarskii type inverse elliptic problem with Dirichlet conditions
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.
AtıfScopus4WoS4OpenAlex3İncele - MakaleAçık Erişim2015Scopus SJRQ3Approximation 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.
AtıfScopus18WoS14OpenAlex18İncele - 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.
AtıfScopus3WoS3OpenAlex3İncele - MakaleAçık Erişim2014Scopus SJRQ2High 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.
AtıfScopus30WoS29OpenAlex26İncele - MakaleAçık Erişim2014Scopus SJRQ2High 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.
AtıfScopus35WoS31OpenAlex35İncele - 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.
AtıfScopus4WoS4OpenAlex5İncele - 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.
AtıfScopus17WoS14OpenAlex16İncele