Stability of a family of difference schemes for the Samarskii-Ionkin problem with variable coefficient

We consider a one-parameter family of difference schemes approximating a nonlocal heat problem with variable coefficient. We study the spectral properties of the main difference operator of the scheme. An energy norm in which the schemes are uniformly stable is defined on the space of grid functions...

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Bibliographic Details
Published in:Differential equations 2014-02, Vol.50 (2), p.254-263
Main Author: Mokin, A. Yu
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Coefficients
Difference and Functional Equations
Differential equations
Eigenvalues
Inequality
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Numerical Methods
Operators
Ordinary Differential Equations
Partial Differential Equations
Spectra
Stability
Studies
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Description
Summary:We consider a one-parameter family of difference schemes approximating a nonlocal heat problem with variable coefficient. We study the spectral properties of the main difference operator of the scheme. An energy norm in which the schemes are uniformly stable is defined on the space of grid functions. The corresponding stability condition is derived.
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226611402013X