Resumen
Hyperbolic equations with unbounded coefficients and even generalized functions (in particular, Dirac-delta functions) occur both naturally and artificially and must be treated in numerical schemes. An abstract operator method is proposed for studying these equations. For finite difference schemes approximating several one-dimensional initial-boundary value problems convergence rate estimates in special discrete energetic Sobolev's norms, compatible with the smoothness of the solutions, are obtained.