Stability of difference schemes for parabolic equations with dynamical boundary conditions and conditions on conjugation

In this paper we investigate the stability of two-level difference schemes for parabolic equations with dynamical boundary conditions and conditions on conjugation. Energy norms that rely on spectral problems containing the eigenvalue in the boundary conditions or conditions on conjugation are introduced. Necessary and sufficient stability conditions in these norms for weighted difference schemes are established. The introducing of appropriate discrete spectral problems enable us to precise the values of the mesh steps that control stability of the difference schemes. Numerical tests are discussed.