On a second order of accuracy stable difference scheme for the solution of a source identification problem for hyperbolic-parabolic equations

2016 ◽  
Author(s):  
Maral Ashyralyyeva ◽  
Maksat Ashyraliyev
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Order Of Accuracy

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Second Order ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
Implicit Difference Scheme ◽  
Order Of Accuracy

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.

scholarly journals On the Crank-Nicolson difference scheme for the time-dependent source identification problem

2021 ◽  
Vol 102 (2) ◽  
pp. 35-44
Author(s):  
A. Ashyralyev ◽  
◽  
M. Urun ◽  
◽  
◽  
...  
Keyword(s):  
Difference Scheme ◽  
Source Identification ◽  
Identification Problem ◽  
Stability Estimates ◽  
Differential Problem ◽  
Order Of Accuracy ◽  
Local Boundary ◽  
Non Local ◽  
The One ◽  
Crank Nicolson

In this study the source identification problem for the one-dimensional Schr¨odinger equation with non-local boundary conditions is considered. A second order of accuracy Crank-Nicolson difference scheme for the numerical solution of the differential problem is presented. Stability estimates are proved for the solution of this difference scheme. Numerical results are given.

Source identification problems for hyperbolic differential and difference equations

2019 ◽  
Vol 27 (3) ◽  
pp. 301-315 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fathi Emharab
Keyword(s):  
Difference Scheme ◽  
Source Identification ◽  
Identification Problem ◽  
Stability Estimates ◽  
Identification Problems ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
First Order ◽  
Accuracy Difference ◽  
The Difference

Abstract In the present study, a source identification problem for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the source identification problem are established. Furthermore, a first-order-of-accuracy difference scheme for the numerical solution of the source identification problem is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example, and some numerical results are presented.

scholarly journals On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Approximate Solution ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Parabolic Problems ◽  
Well Posedness ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
Accuracy Difference

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem−d2u(t)/dt2+Au(t)=g(t),(0≤t≤1),du(t)/dt−Au(t)=f(t),(−1≤t≤0),u(1)=u(−1)+μfor differential equations in a Hilbert spaceHwith a self-adjoint positive definite operatorAis considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.

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