A third order of accuracy difference scheme for the Neumann type overdetermined elliptic problem

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Difference Scheme ◽  
Elliptic Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Neumann Type ◽  
Accuracy Difference

scholarly journals A fourth order approximation of the Neumann type overdetermined elliptic problem

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Order Approximation ◽  
Solution Stability ◽  
Stability Estimates ◽  
Difference Problem ◽  
Neumann Type ◽  
Accuracy Difference ◽  
Coercive Stability

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.

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

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