Speaker
Description
Exponential splitting is a well established and widely used technique for finding approximate solutions of linear DE of type u’=(A+B)u. It can be also used for the case of time dependent component B(t) after application of mid-point quadrature, where the error estimate is not clear in the case of singular cases of unbounded operators B(t).
In this talk I will show how second and fourth order splitting for possibly time dependent component can be derived using Duhamel formula. Based on this approach I will present a new proof of convergence of this scheme and elaborate on the possibilities brought by this approach. Analysis of the error estimated will be presented on the example of hydrogen atom featuring Coulomb potential. Results of numerical simulations will be presented.
