scholarly journals Finite-difference method for the hyperbolic system of equations with nonlocal boundary conditions

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Rahat Prenov
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Hyperbolic System ◽  
Difference Method ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
System Of Equations ◽  
Hyperbolic System Of Equations

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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