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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/846582 |
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| _version_ | 1850177963461443584 |
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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. |
| format | Article |
| id | doaj-art-bcfc04d334ff46f7a2bd41163d9db348 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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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