Abstract
The article presents a brief review of the stability theory of finite-difference schemes for time-dependent problems of mathematical physics in which the spatial differential operator is constrained by boundary conditions joined on different pieces of the boundary. It is shown for the particular case of the heat-conduction equation that nonlocal boundary conditions may generate both simple finite-difference operators and finite-difference operators with an incomplete eigenfunction system. In both cases a rule is suggested for constructing the energy norm that ensures stability of the finite-difference scheme.
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