This paper is devoted to the numerical analysis of inverse problems for abstract hyperbolic differential equations. The presentation exploits general approximation scheme and is based on $C_0$-cosine and $C_0$-semigroup theory within a functional analysis approach. We consider both discretizations as well as in space and time. The discretization in time is considered under the Krein-Fattorini conditions.

Ключевые слова: abstract differential equations, abstract hyperbolic problems, $C_0$-semigroups, $C_0$-cosine operator functions, Banach spaces, semidiscretization, inverse overdetermined problem, well-posedness, difference schemes, discrete semigroups.