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Dimension splitting for time dependent operators

Pages: 322 - 332, Issue Special, September 2009

 Abstract        Full Text (162.8K)              

Eskil Hansen - Institut für Mathematik, Universität Innsbruck, Technikerstraβe 13, A-6020 Innsbruck, Austria (email)
Alexander Ostermann - 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
Mathematics Subject Classification:  Primary: 65M12; Secondary: 65L05, 65J10

Received: August 2008;      Revised: April 2009;      Published: September 2009.