Eskil Hansen - Institut für Mathematik, Universität Innsbruck, Technikerstraβe 13, A-6020 Innsbruck, Austria (email)
Abstract: In this paper we are concerned with the convergence analysis of splitting methods for nonautonomous abstract evolution equations. We introduce a framework that allows us to analyze the popular Lie, Peaceman--Rachford and Strang splittings for time dependent operators. Our framework is in particular suited for analyzing dimension splittings. The influence of boundary conditions is discussed.
Keywords: Nonautonomous linear problems, dimension splitting,
Lie splitting, exponential splitting, Peaceman--Rachford splitting,
stability, convergence, variable time steps
Received: August 2008; Revised: April 2009; Published: September 2009.