Stability estimates for solution of Bitsadze-Samarskii type inverse elliptic problem with Dirichlet conditions

2016 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Gulzipa Akyüz
Keyword(s):  
Elliptic Problem ◽  
Stability Estimates ◽  
Dirichlet Conditions ◽  
Inverse Elliptic Problem

A globally convergent numerical method for an inverse elliptic problem of optical tomography

2010 ◽  
Vol 89 (6) ◽  
pp. 861-891 ◽  
Author(s):  
Michael V. Klibanov ◽  
Jianzhong Su ◽  
Natee Pantong ◽  
Hua Shan ◽  
Hanli Liu
Keyword(s):  
Numerical Method ◽  
Elliptic Problem ◽  
Optical Tomography ◽  
Globally Convergent ◽  
Inverse Elliptic Problem

scholarly journals Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 859-872
Author(s):  
Charyyar Ashyralyyev ◽  
Gulzipa Akyuz
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Elliptic Problem ◽  
Difference Method ◽  
Nonlocal Boundary ◽  
Three Dimensional ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Dirichlet Conditions ◽  
Accuracy Difference

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.

scholarly journals High order approximation of the inverse elliptic problem with Dirichlet-Neumann conditions

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 947-962 ◽  
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Inverse Problem ◽  
Order Approximation ◽  
High Order ◽  
Difference Schemes ◽  
Stability Estimates ◽  
High Order Approximation ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Inverse Elliptic Problem ◽  
Coercive Stability

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.

scholarly journals A note on well-posedness of source identification elliptic problem in a Banach space

2020 ◽  
Vol 99 (3) ◽  
pp. 96-104
Author(s):  
A. Ashyralyev ◽  
◽  
C. Ashyralyyev ◽  
V.G. Zvyagin ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Elliptic Problem ◽  
Source Identification ◽  
Elliptic Equations ◽  
Identification Problem ◽  
Stability Estimates ◽  
Well Posedness ◽  
Identification Problems ◽  
Coercive Stability

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 H¨older 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.

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