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JOURNALS // Nanosystems: Physics, Chemistry, Mathematics // Archive

Nanosystems: Physics, Chemistry, Mathematics, 2017 Volume 8, Issue 2, Pages 202–215 (Mi nano26)

This article is cited 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

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.

PACS: 02.30.Sa,02.30.Tb,02.60.Cb

Received: 19.01.2017
Revised: 29.01.2017

Language: English

DOI: 10.17586/2220-8054-2017-8-2-202-215



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