Yazarlar
Yayınlar
- 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 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 - 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.
- 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 - 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 künye2012Finite difference method for the reverse parabolic problem with Neumann condition
Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar; Ashyralyev, A; Lukashov, A
A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Neumann condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.
AtıfScopus16WoS15OpenAlex11İncele