Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

Allaberen Ashyralyev; Haitham Al-Hazaimeh; Charyyar Ashyralyyev

doi:10.1007/s40314-023-02478-5

Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

Allaberen Ashyralyev, Haitham Al-Hazaimeh, Charyyar Ashyralyyev

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.

Original language	English
Article number	333
Journal	Computational and Applied Mathematics
Volume	42
Issue number	8
DOIs	https://doi.org/10.1007/s40314-023-02478-5
Publication status	Published - Dec 2023
Externally published	Yes

Keywords

Absolute stability
Difference schemes
Source identification problems
Telegraph equations

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10.1007/s40314-023-02478-5

Cite this

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title = "Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem",

abstract = "In the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.",

keywords = "Absolute stability, Difference schemes, Source identification problems, Telegraph equations",

author = "Allaberen Ashyralyev and Haitham Al-Hazaimeh and Charyyar Ashyralyyev",

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doi = "10.1007/s40314-023-02478-5",

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T1 - Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

AU - Ashyralyev, Allaberen

AU - Al-Hazaimeh, Haitham

AU - Ashyralyyev, Charyyar

PY - 2023/12

Y1 - 2023/12

N2 - In the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.

AB - In the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.

KW - Absolute stability

KW - Difference schemes

KW - Source identification problems

KW - Telegraph equations

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DO - 10.1007/s40314-023-02478-5

M3 - Article

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SN - 2238-3603

VL - 42

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 8

M1 - 333

ER -

Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

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Keywords

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Studies from Bahcesehir University Reveal New Findings on Computational and Applied Mathematics (Absolute Stability of a Difference Scheme for the Multidimensional Time-dependently Identification Telegraph Problem)

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Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

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Studies from Bahcesehir University Reveal New Findings on Computational and Applied Mathematics (Absolute Stability of a Difference Scheme for the Multidimensional Time-dependently Identification Telegraph Problem)

Cite this