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Connections in Geometric Numerical Integration

Banff International Research Station for Mathematical Innovation and Discovery

B-series are a special form of Taylor series, where the terms are indexed by rooted trees. The theory originated by the seminal work on numerical integration by John Butcher half a century ago. The theory has developed to become arguably the most important tool in the study of structure preservation of numerical integrators. Geometrically B-series are intimately connected to the geometry of Euclidean spaces. Lie-Butcher series is a generalisation which combines B-series with Lie series, aimed at the study of flows on manifolds. In this talk we will discuss the interplay between the algebraic and geometric structures underlying Lie-Butcher series. We will review various recent results and work in progress, both for ODEs and in the theory of Rough Paths (stochastic DEs).

Mathematics; Numerical analysis

video/mp4

Author affiliation: University of Bergen Norway

2017-12-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63889

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/