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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |