Vasylyk, V.B.2016-04-132016-04-132010-03http://er.nau.edu.ua/handle/NAU/19118A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral for vector-valued functions. This technique translates the initial problem to a system of integral equations. Then the system is approximated with exponential accuracy. The theoretical results are illustrated by examples associated with the heat transfer boundary value problems.enFirst order differential equations in Banach spaceoperator coefficient with a variable domainArticle