scholarly journals Finite Difference Method for the Reverse Parabolic Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Ayfer Dural ◽  
Yasar Sozen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Parabolic Problem ◽  
Dirichlet Condition ◽  
Parabolic Differential Equation ◽  
Stability Estimates ◽  
Accuracy Difference ◽  
Multipoint Boundary Condition ◽  
Coercive Stability

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet 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.

scholarly journals Approximate Solution of Inverse Problem for Elliptic Equation with Overdetermination

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Mutlu Dedeturk
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Stability Estimates ◽  
Two Dimensional ◽  
Accuracy Difference ◽  
Coercive Stability

A…finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied. Stability and coercive stability estimates of the fi…rst and second orders of accuracy difference schemes for this problem are established. The algorithm for approximate solution is tested in a two-dimensional inverse 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.

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