Abstract
We consider an initial-boundary value problem for the heat equation with nonlocal boundary conditions containing a parameter γ > 1. The spectrum of the main differential operator contains some number (depending on γ) of eigenvalues lying in the left complex half-plane, which results in the instability of the problem with respect to the initial data. For difference schemes approximating the original problem, we obtain a criterion for stability in the subspaces generated by stable harmonics.
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