American Institute of Mathematical Sciences

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2009, 2009(Special): 322-332. doi: 10.3934/proc.2009.2009.322

Dimension splitting for time dependent operators

Eskil Hansen 1, and  Alexander Ostermann 1,

1. 

Institut für Mathematik, Universität Innsbruck, Technikerstraβe 13, A-6020 Innsbruck, Austria, Austria

Received  August 2008 Revised  April 2009 Published  September 2009

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: variable time steps, Lie splitting, stability, Peaceman--Rachford splitting, convergence, exponential splitting, dimension splitting, Nonautonomous linear problems.
Mathematics Subject Classification: Primary: 65M12; Secondary: 65L05, 65J10.
Citation: Eskil Hansen, Alexander Ostermann. Dimension splitting for time dependent operators. Conference Publications, 2009, 2009 (Special) : 322-332. doi: 10.3934/proc.2009.2009.322
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