On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations
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,
operatornorm convergence,
convergence rate,
operator splitting
Supporting agencies: The preparation of the paper was supported by the European Research Council via ERC-2010-AdG No. 267802 (“Analysis of Multiscale Systems Driven by Functionals”).
About the Authors
H. Neidhardt
WIAS Berlin
Germany
Germany
Mohrenstr. 39, D-10117 Berlin
A. Stephan
Humboldt Universitat zu Berlin Institut fur Mathematik
Germany
Germany
Unter den Linden 6, D-10099 Berlin
V. A. Zagrebnov
Universite d’Aix-Marseille and Institut de Mathematiques de Marseille (I2M)
France
France
UMR 7373, CMI – Technopole Chateau-Gombert, 13453 Marseille
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Review
For citations:
Neidhardt H., Stephan A., Zagrebnov V.A. On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(2):202-215. https://doi.org/10.17586/2220-8054-2017-8-2-202-215
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