Geodesic
On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations
Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 2, pp. 202-215.

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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: non-autonomous Cauchy problem, solution operators (propagators), Trotter product approximation, operator-norm convergence, operator splitting.
Mots-clés : Evolution equations, convergence rate 
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     author = {H. Neidhardt and A. Stephan and V. A. Zagrebnov},
     title = {On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {202--215},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2017_8_2_a6/}
}
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H. Neidhardt; A. Stephan; V. A. Zagrebnov. On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations. Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 2, pp. 202-215. http://geodesic.mathdoc.fr/item/NANO_2017_8_2_a6/