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

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 space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference sch...

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Main Authors: Allaberen Ashyralyev, Ozgur Yildirim
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/846582
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author Allaberen Ashyralyev
Ozgur Yildirim
author_facet Allaberen Ashyralyev
Ozgur Yildirim
author_sort Allaberen Ashyralyev
collection DOAJ
description 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 space H with the self-adjoint positive definite operator A. 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.
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spelling doaj-art-bcfc04d334ff46f7a2bd41163d9db3482025-08-20T02:18:51ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/846582846582A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic ProblemAllaberen Ashyralyev0Ozgur Yildirim1Department of Mathematics, Fatih University, Buyukcekmece 34500, Istanbul, TurkeyDepartment of Mathematics, Yildiz Technical University, Esenler 34210, Istanbul, TurkeyThe second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert space H with the self-adjoint positive definite operator A. 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.http://dx.doi.org/10.1155/2012/846582
spellingShingle Allaberen Ashyralyev
Ozgur Yildirim
A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
Abstract and Applied Analysis
title A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
title_full A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
title_fullStr A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
title_full_unstemmed A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
title_short A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem
title_sort note on the second order of accuracy stable difference schemes for the nonlocal boundary value hyperbolic problem
url http://dx.doi.org/10.1155/2012/846582
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