This paper is devoted to regularization of derivative’s approximation of integrated semigroups in time variables. We consider the direct method and also the method based on A.N. Tikhonov’s approach. It is shown that the discrete derivative converges in strong sense and the order of convergence in general Banach space is obtained. 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, integrated semigroups, discretization methods, stability of divergence schemes, discrete semigroups, Banach spaces, regularization procedure, ill-posed problems