ИСТИНА

The difference schemes with weights for the heat conduction equation with nonlocal boundary conditions containing a parameter $\gamma$ are discussed. In some intervale $\gamma \in (\gamma _1,\,\gamma _2) $ the spectrum of the differential operator contains three eigenvalues in the left complex half-plane, while the remaining eigenvalues are located in the right half-plane. Earlier a range of $\gamma \in (1,\;\gamma _1)$ was considered in which only one eigenvalue $\lambda _0 $ was located in the left half-plane. The stability criterion of difference schemes is formulated in the subspace induced by stable harmonics.