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Nanosystems: Physics, Chemistry, Mathematics, 2017, Volume 8, Issue 2, Pages 202–215
DOI: https://doi.org/10.17586/2220-8054-2017-8-2-202-215 (Mi nano26) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations

H. Neidhardta, A. Stephanb, V. A. Zagrebnovc

a WIAS Berlin, Mohrenstr. 39, D10117 Berlin, Germany
b Humboldt Universität zu Berlin, Institut für Mathematik Unter den Linden 6, D10099 Berlin, Germany
c Université d'Aix-Marseille and Institut de Mathématiques de Marseille (I2M) UMR 7373, CMI – Technopôle Château-Gombert, 13453 Marseille, France
Full-text PDF (253 kB) Citations (5)
DOI: https://doi.org/10.17586/2220-8054-2017-8-2-202-215
Abstract: We improve some recent estimates of the rate of convergence for product approximations of solution operators for linear non-autonomous Cauchy problem. The Trotter product formula approximation is proved to converge to the solution operator in the operator-norm. We estimate the rate of convergence of this approximation. The result is applied to diffusion equation perturbed by a time-dependent potential.
Keywords: Evolution equations, non-autonomous Cauchy problem, solution operators (propagators), Trotter product approximation, operator-norm convergence, convergence rate, operator splitting.
Funding agency Grant number
European Research Council 267802
The preparation of the paper was supported by the European Research Council via ERC-2010-AdG №. 267802 (“Analysis of Multiscale Systems Driven by Functionals”).
Received: 19.01.2017
Revised: 29.01.2017
Bibliographic databases:
Document Type: Article
PACS: 02.30.Sa,02.30.Tb,02.60.Cb
Language: English
Citation: H. Neidhardt, A. Stephan, V. A. Zagrebnov, “On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations”, Nanosystems: Physics, Chemistry, Mathematics, 8:2 (2017), 202–215
Citation in format AMSBIB
\Bibitem{NeiSteZag17}
\by H.~Neidhardt, A.~Stephan, V.~A.~Zagrebnov
\paper On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2017
\vol 8
\issue 2
\pages 202--215
\mathnet{http://mi.mathnet.ru/nano26}
\crossref{https://doi.org/10.17586/2220-8054-2017-8-2-202-215}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000412772000007}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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