This paper provides a unified error analysis for nonconforming space discretizations of
linear wave equations in the time domain. We propose a framework that studies wave …

The choice of the location of controllers and observations is of great importance for
designing control systems and improving the estimations in various practical problems. For …

This paper is an extended and reworked version of a short course given by the author
at''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was …

Abstract k] We show that the abstract operator-theoretic (general) Trotter–Kato formulae
yield the convergence of numerical methods used for solving differential equations. These …

Abstract We investigate Lie–Trotter product formulae for abstract nonlinear evolution
equations with delay. Using results from the theory of nonlinear contraction semigroups in …

We present easy to verify conditions implying stability estimates for operator matrix splittings
which ensure convergence of the associated Trotter, Strang and weighted product formulas …

The stability is one of the most basic requirement for the numerical model, which is mostly
elaborated for the linear problems. In this paper we analyze the stability notions for the …

The Douglas-Rachford and Peaceman-Rachford splitting methods are common choices for
temporal discretizations of evolution equations. In this paper we combine these methods …

The mathematical study of dynamical systems in discrete or continuous time on spaces of
probability measures has a long-lasting history in probability theory (as Markov operators …

The paper serves as a review on the basic results showing how functional analytic tools
have been applied in numerical analysis. It deals with abstract Cauchy problems and …