Numerical approaches for solution of hyperbolic difference equations on circle

Allaberen Ashyralyev; Fatih Hezenci; Yasar Sozen

doi:10.1515/gmj-2023-2103

Numerical approaches for solution of hyperbolic difference equations on circle

Allaberen Ashyralyev
, Fatih Hezenci
, Yasar Sozen

Division of Topology

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

Abstract

The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T¹. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.

Original language	English
Pages (from-to)	723-730
Number of pages	8
Journal	Georgian Mathematical Journal
Volume	31
Issue number	5
DOIs	https://doi.org/10.1515/gmj-2023-2103
Publication status	Published - 1 Oct 2024

Keywords

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

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10.1515/gmj-2023-2103

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abstract = "The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T1. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various H{\"o}lder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.",

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AU - Sozen, Yasar

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N2 - The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T1. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.

AB - The present paper considers nonlocal boundary value problems for hyperbolic equations on the circle T1. The first-order modified difference scheme for the numerical solution of nonlocal boundary value problems for hyperbolic equations on a circle is presented. The stability and coercivity estimates in various Hölder norms for solutions of the difference schemes are established. Moreover, numerical examples are provided.

KW - Difference equations on manifolds

KW - difference schemes

KW - self-adjoint positive definite operator

KW - well-posedness

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JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

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ER -

Numerical approaches for solution of hyperbolic difference equations on circle

Abstract

Keywords

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