A third order of accuracy difference scheme for Bitsadze-Samarskii type elliptic overdetermined multi-point problem

2018 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Gulzıpa Akyüz
Keyword(s):  
Difference Scheme ◽  
Point Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Accuracy Difference

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.

The Comparison for Several Difference Methods in Heat Conduction Equations

2011 ◽  
Vol 282-283 ◽  
pp. 399-402
Author(s):  
Fan Lei Meng
Keyword(s):  
Heat Conduction ◽  
Difference Scheme ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
High Accuracy ◽  
Third Order ◽  
Numerical Experimentation ◽  
Valuable Method ◽  
Accuracy Difference ◽  
Initial Boundary Value

In this paper, one-dimensional heat conduction equations is studied, many difference Schemes have been proposed to solve it. In order to find a high accuracy difference scheme in all the methods, we give a numerical experimentation in this paper. by numerical experimentation, a high accuracy difference scheme for solving Heat conduction equations initial boundary value problem is found, according to the truncation error and stability analysis ,we find its accuracy is better-then- third-order in time and space direction. this is a valuable method and better then the others this is a high accuracy difference Scheme. this scheme is a valuable method in Heat conduction and Fluid mechanics.

scholarly journals On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem

2021 ◽  
Vol 102 (2) ◽  
pp. 45-53
Author(s):  
C. Ashyralyyev ◽  
◽  
G. Akyuz ◽  
◽  
Keyword(s):  
Approximate Solution ◽  
Difference Scheme ◽  
Fourth Order ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Uniqueness Of The Solution ◽  
Accuracy Difference ◽  
The Difference ◽  
Overdetermined Boundary Value Problem ◽  
Coercive Stability

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.

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