Conveners
Splitting Methods on Unbounded Domains
- Karolina Kropielnicka (University of Gdańsk)
Description
Exponential splitting methods are well-established tools for the numerical approximation of partial differential equations. They are commonly used for time discretisation in situations where the differential equation can be decomposed into two (or more) subproblems, each of which can be treated efficiently, either numerically or even analytically.
The most common approaches to their derivation and rigorous analysis rely on Taylor expansions or the Baker–Campbell–Hausdorff formula. However, the convergence of these methods is guaranteed only in the case of bounded operators. When unbounded domains are considered, this assumption is naturally violated.
In this talk, I will present the ideas behind the derivation and rigorous analysis of Strang splittings, compact splittings, and finally focus on symmetric Zassenhaus splittings. These methods are particularly advantageous for time-dependent linear Schrödinger equations, although the analysis will be carried out in the setting of general operators.
