On convergence rate estimates for approximations of solution operators of linear non-autonomous evolution equations

Hagen A Neidhardt (1) , Artur A Stephan (2) , Valentin A Zagrebnov (3)

1 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
2 Institut für Mathematik [Humboldt]
3 I2M - Institut de Mathématiques de Marseille

We improve some recent convergence rate estimates for approximations of solution operators of linear non-autonomous evolution equations. The approximation results from the Trotter product formula which is proved to converge in the operator-norm and its convergence can be estimated. The result is applied to a diffusion perturbed by a time-dependent potential.

Mots clés: operator splitting; approximation; convergence rate; Trotter product formula; evolution equations; operator-norm topology

Domaines: Analyse fonctionnelle [math.FA]

Hagen A Neidhardt, Artur A Stephan, Valentin A Zagrebnov. On convergence rate estimates for approximations of solution operators of linear non-autonomous evolution equations. Nanosystems: Physics, Chemistry, Mathematics, 2017, 8 (2), pp.202 - 215. ⟨10.17586/2220-8054-2017-8-2-202-215⟩. ⟨hal-01418846⟩