A Note on Stability of Parabolic Difference Equations on Torus

Allaberen Ashyralyev; Fatih Hezenci; Yasar Sozen

doi:10.1080/01630563.2023.2183509

A Note on Stability of Parabolic Difference Equations on Torus

Allaberen Ashyralyev
, Fatih Hezenci
, Yasar Sozen

Division of Topology

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

1 Citation (Scopus)

Abstract

The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.

Original language	English
Pages (from-to)	490-509
Number of pages	20
Journal	Numerical Functional Analysis and Optimization
Volume	44
Issue number	6
DOIs	https://doi.org/10.1080/01630563.2023.2183509
Publication status	Published - 2023

Keywords

Difference equations on manifolds
difference schemes
self-adjoint positive definite operator
well-posedness

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10.1080/01630563.2023.2183509

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title = "A Note on Stability of Parabolic Difference Equations on Torus",

abstract = "The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various H{\"o}lder norms are established. Furthermore, theoretical results are supported by numerical experiments.",

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AU - Hezenci, Fatih

AU - Sozen, Yasar

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Y1 - 2023

N2 - The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.

AB - The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.

KW - Difference equations on manifolds

KW - difference schemes

KW - self-adjoint positive definite operator

KW - well-posedness

UR - https://www.scopus.com/pages/publications/85149502086

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DO - 10.1080/01630563.2023.2183509

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 6

ER -

A Note on Stability of Parabolic Difference Equations on Torus

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Keywords

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