Yazarlar
- Ashyralyyev, Charyyar(18)
- Ashyralyev, A.(4)
- Ashyralyyev, C.(4)
- Dedeturk, Mutlu(3)
- Lukashov, A.(3)
- Akyuz, G.(2)
- Ashyralyev, A(2)
- Ashyralyev, Allaberen(2)
- Malkowsky, E(2)
- Akkan, Pinar(1)
- Akkan, Yasar(1)
- Akyuz, Gulzipa(1)
- Akyüz, Gulzipa(1)
- Al-Hammouri, Ahmad(1)
- Aral, N.D.(1)
- Basar, F.(1)
- Cakalli, H.(1)
- Canak, I.(1)
- Cay, A.(1)
- Dik, M.(1)
- Gurtug, O.(1)
- G¨onenc¸, Ahmet(1)
- Harte, R.(1)
- Kandemir, H.S.(1)
- Kocinac, L.D.R.(1)
- Malkowsky, E.(1)
- Onvural, O.R.(1)
- Sahin, H.(1)
- Sahinaslan, O.(1)
- Savas, E.(1)
- Sezer, S.A.(1)
- Tez, M.(1)
- Turkoglu, A.D.(1)
- Ucgan, F.C.(1)
Yayınlar
- MakaleAçık Erişim2022Scopus SJRQ2On the second order of accuracy stable difference scheme for integral type non-local elliptic source identification problem
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.
AtıfScopus2WoS1OpenAlex2
İncele - BildiriYalnız künye2022Numerical Solution of Time-Nonlocal Problem for Parabolic Equation
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.
AtıfScopus2OpenAlex3İncele - 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.
AtıfOpenAlex1İncele - MakaleYalnız künye2021Scopus SJRQ2On the absolute stable difference scheme for the space-wise dependent source identification problem for elliptic-telegraph equation
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.
AtıfScopus27WoS13OpenAlex23İncele - MakaleAçık Erişim2021Scopus SJRQ3Crank-nicolson difference scheme for reverse parabolic nonlocal problem with integral and neumann boundary conditions
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.
AtıfScopus5OpenAlex3İncele - 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.
AtıfOpenAlex5İncele - MakaleAçık Erişim2020Scopus SJRQ3The second order of ADS for reverse parabolic boundary value problem with integral condition
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.
AtıfScopus4WoS1OpenAlex5İncele - MakaleYalnız künye2020Scopus SJRQ2Source Identification Problem for a Parabolic Equation with Multipoint Nonlocal Boundary Condition
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.
AtıfScopus7WoS6OpenAlex7İncele - MakaleYalnız künye2020Scopus SJRQ1Stability of Rothe difference scheme for the reverse parabolic problem with integral boundary condition
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.
AtıfScopus9WoS6OpenAlex9İncele - 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 - MakaleYalnız künye2017Scopus SJRQ3Approximate 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.
AtıfScopus22WoS19İncele - MakaleAçık Erişim2017Scopus SJRQ3Numerical 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.
AtıfScopus30WoS23OpenAlex27İncele - 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 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 - MakaleYalnız künye2015Scopus SJRQ3Numerical 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.
AtıfScopus22WoS19İncele - 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