scholarly journals A note on the hyperbolic-parabolic identification problem with involution and Dirichlet boundary condition

2020 ◽  
Vol 99 (3) ◽  
pp. 120-129
Author(s):  
Maksat Ashyraliyev ◽  
◽  
Maral A. Ashyralyyeva ◽  
Allaberen Ashyralyev ◽  
◽  
...  
Keyword(s):  
Source Identification ◽  
Test Problem ◽  
Dirichlet Boundary ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Simple Test ◽  
Order Of Accuracy ◽  
First Order ◽  
The Stability

In the present paper, a source identification problem for hyperbolic-parabolic equation with involution and Dirichlet condition is studied. The stability estimates for the solution of the source identification hyperbolicparabolic problem are established. The first order of accuracy stable difference scheme is constructed for the approximate solution of the problem under consideration. Numerical results are given for a simple test problem.

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.

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 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.

scholarly journals A note on the parabolic identification problem with involution and Dirichlet condition

2020 ◽  
Vol 99 (3) ◽  
pp. 130-139
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
A. Sarsenbi ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Difference Scheme ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Dirichlet Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
The Difference

A space source of identification problem for parabolic equation with involution and Dirichlet condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem is presented. Furthermore, stability estimates for the difference scheme of the source identification parabolic problem are presented. Numerical results are given.

scholarly journals On the stability of the telegraph equation with time delay

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1251-1259
Author(s):  
Allaberen Ashyralyev ◽  
Deniz Agirseven ◽  
Koray Turk
Keyword(s):  
Boundary Condition ◽  
Time Delay ◽  
Test Problem ◽  
Dirichlet Boundary ◽  
Telegraph Equation ◽  
Stability Estimates ◽  
Initial Value ◽  
One Dimensional ◽  
Telegraph Equations ◽  
The Stability

In this study, the initial value problem for telegraph equations with time delay in a Hilbert space is considered. The main theorem on stability estimates for the solution of this problem is established. As a test problem, one-dimensional delay telegraph equation with the Dirichlet boundary condition is considered.

scholarly journals A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Ozgur Yildirim
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Hyperbolic Problem ◽  
Definite Operator ◽  
The Stability

The second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert spaceHwith the self-adjoint positive definite operatorA. The stability estimates for the solutions of these difference schemes are established. In practice, one-dimensional hyperbolic equation with nonlocal boundary conditions and multidimensional hyperbolic equation with Dirichlet conditions are considered. The stability estimates for the solutions of these difference schemes for the nonlocal boundary value hyperbolic problem are established. Finally, a numerical method proposed and numerical experiments, analysis of the errors, and related execution times are presented in order to verify theoretical statements.

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.

scholarly journals Parabolic time dependent source identification problem with involution and Neumann condition

2021 ◽  
Vol 102 (2) ◽  
pp. 5-15
Author(s):  
A. Ashyralyev ◽  
◽  
A.S. Erdogan ◽  
◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Parabolic Equation ◽  
Source Identification ◽  
Parabolic Problem ◽  
Identification Problem ◽  
Time Dependent ◽  
Neumann Condition ◽  
Stability Estimates ◽  
Well Posedness

A time dependent source identification problem for parabolic equation with involution and Neumann condition is studied. The well-posedness theorem on the differential equation of the source identification parabolic problem is established. The stable difference scheme for the approximate solution of this problem and its stability estimates are presented. Numerical results are given.

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