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Stability criterion for a family of nonlocal difference schemes
We consider finite-difference schemes for the heat equation with nonlocal boundary conditions that contain a real parameter γ . A stability criterion for finite-difference schemes with respect to the initial data was earlier obtained for |γ| ≤ 1. In the present paper, we consider the case in which γ...
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Published in: | Differential equations 2010-07, Vol.46 (7), p.973-990 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We consider finite-difference schemes for the heat equation with nonlocal boundary conditions that contain a real parameter
γ
. A stability criterion for finite-difference schemes with respect to the initial data was earlier obtained for
|γ|
≤ 1. In the present paper, we consider the case in which
γ
∈ (−cosh
π
,−1) and the original differential problem is stable, while the stability conditions for the finite-difference schemes substantially depend on
γ
. We obtain estimates for the energy norm of the solution of the finite-difference problem via the same norm of the initial data and prove the equivalence of the energy norm and the grid
L
2
-norm. |
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ISSN: | 0012-2661 1608-3083 |
DOI: | 10.1134/S0012266110070050 |