NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2017, 8 (2), P. 202–215
On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations
H. Neidhardt – WIAS Berlin, Mohrenstr. 39, D-10117 Berlin, Germany; hagen.neidhardt@wiasberlin.de
A. Stephan – Humboldt Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, D-10099 Berlin, Germany; stephan@math.huberlin.de
V. A. Zagrebnov – Université d’AixMarseille and Institut de Mathématiques de Marseille (I2M) UMR 7373, CMI – Technopôle Château-Gombert, 13453 Marseille, France; valentin.zagrebnov@univamu.fr
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
DOI 10.17586/2220-8054-2017-8-2-202-215