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A New Unconditionally Stable Second Order of Accuracy Difference Scheme for the Time Delay Telegraph Equation

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dc.contributor.authorAshyralyev, Allaberen
dc.contributor.authorAǧirseven, Deniz
dc.contributor.authorTurk, Koray
dc.contributor.institutionAshyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
dc.contributor.institutionAǧirseven, Deniz, Department of Mathematics, Trakya Üniversitesi, Edirne, Turkey
dc.contributor.institutionTurk, Koray, Department of Mathematics, Trakya Üniversitesi, Edirne, Turkey
dc.date.accessioned2025-10-05T14:36:01Z
dc.date.issued2025
dc.description.abstractIn this paper, we study a new unconditionally stable second order of accuracy difference scheme for the approximate solution of the initial value problem for the time delay telegraph equation in a Hilbert space with self-adjoint positive definite operator. We prove the main theorem on stability of this difference scheme. As an application, we present absolutely stable difference schemes for the approximate solution of two initial-boundary value problems for one-dimensional delay telegraph equation with nonlocal conditions and multidimensional delay telegraph equation with Dirichlet condition. Finally, to support the theoretical result, a numerical example of the initial-boundary value problem for the two-dimensional delay telegraph equation with Dirichlet condition is presented. © 2025 Elsevier B.V., All rights reserved.
dc.identifier.doi10.1002/mma.70106
dc.identifier.issn01704214
dc.identifier.issn10991476
dc.identifier.scopus2-s2.0-105015561648
dc.identifier.urihttps://doi.org/10.1002/mma.70106
dc.identifier.urihttps://hdl.handle.net/20.500.14719/6630
dc.language.isoen
dc.publisherJohn Wiley and Sons Ltd
dc.relation.sourceMathematical Methods in the Applied Sciences
dc.subject.authorkeywordsDelay Telegraph Equation
dc.subject.authorkeywordsDifference Scheme
dc.subject.authorkeywordsStability
dc.subject.authorkeywordsBoundary Conditions
dc.subject.authorkeywordsConvergence Of Numerical Methods
dc.subject.authorkeywordsInitial Value Problems
dc.subject.authorkeywordsMathematical Operators
dc.subject.authorkeywordsTelegraph
dc.subject.authorkeywordsTime Delay
dc.subject.authorkeywordsTiming Circuits
dc.subject.authorkeywordsAccuracy Difference Schemes
dc.subject.authorkeywordsApproximate Solution
dc.subject.authorkeywordsDelay Telegraph Equation
dc.subject.authorkeywordsDifference Schemes
dc.subject.authorkeywordsInitial-boundary Value Problems
dc.subject.authorkeywordsOrder Of Accuracy
dc.subject.authorkeywordsSecond Orders
dc.subject.authorkeywordsTelegraph Equation
dc.subject.authorkeywordsTime-delays
dc.subject.authorkeywordsUnconditionally Stable
dc.subject.authorkeywordsFinite Difference Method
dc.subject.indexkeywordsBoundary conditions
dc.subject.indexkeywordsConvergence of numerical methods
dc.subject.indexkeywordsInitial value problems
dc.subject.indexkeywordsMathematical operators
dc.subject.indexkeywordsTelegraph
dc.subject.indexkeywordsTime delay
dc.subject.indexkeywordsTiming circuits
dc.subject.indexkeywordsAccuracy difference schemes
dc.subject.indexkeywordsApproximate solution
dc.subject.indexkeywordsDelay telegraph equation
dc.subject.indexkeywordsDifference schemes
dc.subject.indexkeywordsInitial-boundary value problems
dc.subject.indexkeywordsOrder of accuracy
dc.subject.indexkeywordsSecond orders
dc.subject.indexkeywordsTelegraph equation
dc.subject.indexkeywordsTime-delays
dc.subject.indexkeywordsUnconditionally stable
dc.subject.indexkeywordsFinite difference method
dc.titleA New Unconditionally Stable Second Order of Accuracy Difference Scheme for the Time Delay Telegraph Equation
dc.typeArticle
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dspace.entity.typePublication
local.indexed.atScopus
person.identifier.scopus-author-id6602401828
person.identifier.scopus-author-id24553957700
person.identifier.scopus-author-id57192193426

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