Stability of a family of weighted finite-difference schemes

Existence and uniqueness theorems are proved for a weighted finite-difference scheme approximating the heat equation with a nonlocal boundary condition containing a parameter. Bounds are derived that guarantee stability of the solution in the initial values in the mean-square grid norm.

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Bibliographic Details
Published in:Computational mathematics and modeling 2009-04, Vol.20 (2), p.152-172
Main Authors: Gulin, A. V., Mokin, A. Yu
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical Methods
Optimization
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Description
Summary:Existence and uniqueness theorems are proved for a weighted finite-difference scheme approximating the heat equation with a nonlocal boundary condition containing a parameter. Bounds are derived that guarantee stability of the solution in the initial values in the mean-square grid norm.
ISSN:1046-283X
1573-837X
DOI:10.1007/s10598-009-9026-1