This paper is devoted to approximation of integrated semigroups in space and in time variables. The presentation is given in the abstract framework of discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods.

Ключевые слова: abstract differential equations in Banach spaces, $C_0$-semigroups, integrated semigroups, Trotter-Kato theorem, discretization methods, difference schemes, stability of difference schemes, discrete semigroups, Banach spaces.