Dimension splitting for time dependent operators

Eskil Hansen; Alexander Ostermann

doi:10.3934/proc.2009.2009.322

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2009, Volume 2009: 322-332. Doi: 10.3934/proc.2009.2009.322 open access

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Dimension splitting for time dependent operators

Eskil Hansen^1, and
Alexander Ostermann^1,

1.
Institut für Mathematik, Universität Innsbruck, Technikerstraβe 13, A-6020 Innsbruck

Received: August 2008

Revised: April 2009

Published online: September 2009

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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.

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Mathematics Subject Classification: Primary: 65M12; Secondary: 65L05, 65J10.

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