Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations
We consider the abstract Cauchy problem for differential equation of the hyperbolic type v″(t)+Av(t)=f(t) (0≤t≤T), v(0)=v0, v′(0)=v′0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A. The high order of accuracy two-step difference schemes generated by an exact differ...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS.2005.183 |
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| author | Allaberen Ashyralyev Pavel E. Sobolevskii |
| author_facet | Allaberen Ashyralyev Pavel E. Sobolevskii |
| author_sort | Allaberen Ashyralyev |
| collection | DOAJ |
| description | We consider the abstract Cauchy problem for differential equation of the hyperbolic type v″(t)+Av(t)=f(t) (0≤t≤T), v(0)=v0, v′(0)=v′0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on the three points for the numerical solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are established. In applications, the stability estimates for the solutions of the high order of accuracy difference schemes of the mixed-type boundary value problems for hyperbolic equations are obtained. |
| format | Article |
| id | doaj-art-e9c1288058fe41e58a48340bfe62b7c9 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e9c1288058fe41e58a48340bfe62b7c92025-08-20T02:21:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2005-01-012005218321310.1155/DDNS.2005.183Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equationsAllaberen Ashyralyev0Pavel E. Sobolevskii1Department of Mathematics, Fatih University, Buyukcekmece, Istanbul 39400, TurkeyInstitute of Mathematics, Federal University of Ceará, Fortaleza 60020-181, Ceará, BrazilWe consider the abstract Cauchy problem for differential equation of the hyperbolic type v″(t)+Av(t)=f(t) (0≤t≤T), v(0)=v0, v′(0)=v′0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on the three points for the numerical solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are established. In applications, the stability estimates for the solutions of the high order of accuracy difference schemes of the mixed-type boundary value problems for hyperbolic equations are obtained.http://dx.doi.org/10.1155/DDNS.2005.183 |
| spellingShingle | Allaberen Ashyralyev Pavel E. Sobolevskii Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations Discrete Dynamics in Nature and Society |
| title | Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| title_full | Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| title_fullStr | Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| title_full_unstemmed | Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| title_short | Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| title_sort | two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations |
| url | http://dx.doi.org/10.1155/DDNS.2005.183 |
| work_keys_str_mv | AT allaberenashyralyev twonewapproachesforconstructionofthehighorderofaccuracydifferenceschemesforhyperbolicdifferentialequations AT pavelesobolevskii twonewapproachesforconstructionofthehighorderofaccuracydifferenceschemesforhyperbolicdifferentialequations |