On the Stability of Nonlocal Difference Schemes in Subspacesстатья
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Дата последнего поиска статьи во внешних источниках: 2 октября 2014 г.
Аннотация:We consider finite-difference schemes for the heat equation with nonlocal boundary
conditions. The original problem, as well as the approximating finite-difference schemes, is not
stable under perturbations of the initial data. For such problems, we introduce the definition of
stability of a finite-difference scheme in a subspace and derive estimates in terms of Hilbert norms
expressing the stability with respect to the initial data in subspaces spanned by eigenvectors of
the main difference operator.