najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-202-215najo-652Research ArticleMATHEMATICSМАТЕМАТИКАOn convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equationsNeidhardtH.

Mohrenstr. 39, D-10117 Berlin

hagen.neidhardt@wias-berlin.deStephanA.

Unter den Linden 6, D-10099 Berlin

stephan@math.hu-berlin.deZagrebnovV. A.

UMR 7373, CMI – Technopole Chateau-Gombert, 13453 Marseille

valentin.zagrebnov@univ-amu.frWIAS BerlinGermanyHumboldt Universitat zu Berlin Institut fur MathematikGermanyUniversite d’Aix-Marseille and Institut de Mathematiques de Marseille (I2M)France20171208202582202215Copyright © Neidhardt H., Stephan A., Zagrebnov V.A., 20252025Neidhardt H., Stephan A., Zagrebnov V.A.Neidhardt H., Stephan A., Zagrebnov V.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/652

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.

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The authors declare that there are no conflicts of interest present.