The geometric properties of exotic aromatic Butcher-series in stochastic backward error analysis (Adrien Laurent, INRIA Rennes)

16.04.2024 14:00 – 15:00

The Butcher series are a strong tool for the backward error analysis of ordinary and stochastic differential equations. After introducing the standard B-series, their exotic and aromatic extensions, and some of their numerical applications, we will ask ourselves the question: are these B-series just a tool for tedious calculations or are they interesting beyond their numerical applications? We will show that exotic aromatic B-series satisfy a universal geometric property of equivariance, which confirms that they are a natural geometric object that is interesting not only from the numerical point of view. If time allows, we shall quickly discuss the extension of exotic aromatic B-series to the creation of methods on manifolds.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre