Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space
The initial-value problem for hyperbolic equation d2u(t)/dt2+A(t)u(t)=f(t)(0≤t≤T), u(0)=ϕ,u′(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is pre...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/57491 |
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| _version_ | 1832564367183314944 |
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| author | Allaberen Ashyralyev Mehmet Emir Koksal |
| author_facet | Allaberen Ashyralyev Mehmet Emir Koksal |
| author_sort | Allaberen Ashyralyev |
| collection | DOAJ |
| description | The initial-value problem for hyperbolic equation
d2u(t)/dt2+A(t)u(t)=f(t)(0≤t≤T), u(0)=ϕ,u′(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving
this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established. |
| format | Article |
| id | doaj-art-e2ac7892b3264fc69b5d4d26fd022611 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e2ac7892b3264fc69b5d4d26fd0226112025-02-03T01:11:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/5749157491Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert SpaceAllaberen Ashyralyev0Mehmet Emir Koksal1Department of Mathematics, Fatih University, Buyukcekmece, Istanbul 34900, TurkeyGraduate Institute of Sciences and Engineering, Fatih University, Buyukcekmece, Istanbul 34900, TurkeyThe initial-value problem for hyperbolic equation d2u(t)/dt2+A(t)u(t)=f(t)(0≤t≤T), u(0)=ϕ,u′(0)=ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.http://dx.doi.org/10.1155/2007/57491 |
| spellingShingle | Allaberen Ashyralyev Mehmet Emir Koksal Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space Discrete Dynamics in Nature and Society |
| title | Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space |
| title_full | Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space |
| title_fullStr | Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space |
| title_full_unstemmed | Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space |
| title_short | Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space |
| title_sort | stability of a second order of accuracy difference scheme for hyperbolic equation in a hilbert space |
| url | http://dx.doi.org/10.1155/2007/57491 |
| work_keys_str_mv | AT allaberenashyralyev stabilityofasecondorderofaccuracydifferenceschemeforhyperbolicequationinahilbertspace AT mehmetemirkoksal stabilityofasecondorderofaccuracydifferenceschemeforhyperbolicequationinahilbertspace |