Applications of Steklov-type eigenvalue problems to convergence of difference schemes for parabolic and hyperbolic equations with dynamical boundary conditions

Abstract

Parabolic and hyperbolic equations with dynamical boundary conditions, i.e which involve first and second order time derivatives respectively, are considered. Convergence and stability of weighted difference schemes for such problems are discussed. Norms arising from Steklov-type eigenvalues problems are used, while in previously investigations, norms corresponding to Neumann's or Robin's boundary conditions are used. More exact stability conditions are obtained for the difference schemes parameters.