Numerical solution to the second order of accuracy difference scheme for the source identification elliptic-telegraph problem

2021 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ahmad Al-Hammouri
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Source Identification ◽  
Second Order ◽  
Order Of Accuracy ◽  
Accuracy Difference

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 A second order of accuracy difference scheme for Schrödinger equations with an unknown parameter

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 981-993 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mesut Urun
Keyword(s):  
Difference Scheme ◽  
Unknown Parameter ◽  
Second Order ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
Accuracy Difference ◽  
The Stability ◽  
Parameter Problem

In the present study, the second order of accuracy difference scheme for numerical solution of the boundary value problem for the differential equation with an unknown parameter p {idu(t)/dt + Au(t) + iu(t) = f (t) + p, 0 < t < T, u(0) = ? u(T) = ? in a Hilbert space H with self-adjoint positive definite operator A is presented. Theorem on the stability of this difference scheme is established. The stability estimates for the solution of difference schemes for two determination of an unknown parameter problem for Schr?dinger equations 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 Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space

2007 ◽  
Vol 2007 ◽  
pp. 1-25 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mehmet Emir Koksal
Keyword(s):  
Hilbert Space ◽  
Difference Scheme ◽  
Hyperbolic Equation ◽  
Initial Value Problem ◽  
Second Order ◽  
Stability Estimates ◽  
Initial Value ◽  
Order Of Accuracy ◽  
Positive Definite Operators ◽  
Accuracy Difference

The initial-value problem for hyperbolic equation d2u(t)/dt2+A(t)u(t)=f(t)(0≤t≤T), u(0)=ϕ,u′(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.

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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