Well-posedness of the difference schemes of the high order of accuracy for elliptic equations
It is well known the differential equation −u″(t)+Au(t)=f(t)(−∞<t<∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E)=C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ‖ϕ‖C(E)=sup−∞<t<∞‖ϕ(t)‖E. In...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/75153 |
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| author | Allaberen Ashyralyev Pavel E. Sobolevskiĭ |
| author_facet | Allaberen Ashyralyev Pavel E. Sobolevskiĭ |
| author_sort | Allaberen Ashyralyev |
| collection | DOAJ |
| description | It is well known the differential equation −u″(t)+Au(t)=f(t)(−∞<t<∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space
C(E)=C((−∞,∞),E) of the bounded continuous functions
ϕ(t) defined on the whole real line with norm
‖ϕ‖C(E)=sup−∞<t<∞‖ϕ(t)‖E. In the present paper we consider the high order of accuracy
two-step difference schemes generated by an exact difference
scheme or by Taylor's decomposition on three points for the
approximate solutions of this differential equation. The
well-posedness of these difference schemes in the difference
analogy of the smooth functions is obtained. The exact almost
coercive inequality for solutions in C(τ,E) of these difference schemes is established. |
| format | Article |
| id | doaj-art-561d6ceb89e342b58f34e8f06f3a85ae |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-561d6ceb89e342b58f34e8f06f3a85ae2025-02-03T07:24:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/7515375153Well-posedness of the difference schemes of the high order of accuracy for elliptic equationsAllaberen Ashyralyev0Pavel E. Sobolevskiĭ1Department of Mathematics, Fatih University, Istanbul, TurkeyInstitute of Mathematics, Universidade Federal do Ceara, BrazilIt is well known the differential equation −u″(t)+Au(t)=f(t)(−∞<t<∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E)=C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ‖ϕ‖C(E)=sup−∞<t<∞‖ϕ(t)‖E. In the present paper we consider the high order of accuracy two-step difference schemes generated by an exact difference scheme or by Taylor's decomposition on three points for the approximate solutions of this differential equation. The well-posedness of these difference schemes in the difference analogy of the smooth functions is obtained. The exact almost coercive inequality for solutions in C(τ,E) of these difference schemes is established.http://dx.doi.org/10.1155/DDNS/2006/75153 |
| spellingShingle | Allaberen Ashyralyev Pavel E. Sobolevskiĭ Well-posedness of the difference schemes of the high order of accuracy for elliptic equations Discrete Dynamics in Nature and Society |
| title | Well-posedness of the difference schemes of the high order of accuracy for elliptic equations |
| title_full | Well-posedness of the difference schemes of the high order of accuracy for elliptic equations |
| title_fullStr | Well-posedness of the difference schemes of the high order of accuracy for elliptic equations |
| title_full_unstemmed | Well-posedness of the difference schemes of the high order of accuracy for elliptic equations |
| title_short | Well-posedness of the difference schemes of the high order of accuracy for elliptic equations |
| title_sort | well posedness of the difference schemes of the high order of accuracy for elliptic equations |
| url | http://dx.doi.org/10.1155/DDNS/2006/75153 |
| work_keys_str_mv | AT allaberenashyralyev wellposednessofthedifferenceschemesofthehighorderofaccuracyforellipticequations AT pavelesobolevskii wellposednessofthedifferenceschemesofthehighorderofaccuracyforellipticequations |