The Butcher group is a powerful tool for analysing integration methods for ordinary differential equations, in particular Runge-Kutta methods. Recently, a natural Lie group structure has been constructed for this group. Unfortunately, the associated topology is too coarse for some applications in numerical analysis. In the present paper, we propose to remedy this problem by replacing the Butcher group with the subgroup of all exponentially bounded elements. This "tame Butcher group" turns out to be an infinite-dimensional Lie group with respect to a finer topology. As a first application, we show that the correspondence of elements in the tame Butcher group with their associated B-series induces certain Lie group (anti)morphisms.
Classification :
22E65, 65L06, 58A07
Mots-clés :
Butcher group, infinite-dimensional Lie group, Silva space, regularity of Lie groups, B-series, group of germs of diffeomorphisms
Affiliations des auteurs :
Geir Bogfjellmo
1
;
Alexander Schmeding
1
1
NTNU Trondheim, Alfred Getz' vei 1, 7491 Trondheim, Norway
Geir Bogfjellmo; Alexander Schmeding. The Tame Butcher Group. Journal of Lie Theory, Tome 26 (2016) no. 4, pp. 1107-1144. http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a7/
@article{JOLT_2016_26_4_a7,
author = {Geir Bogfjellmo and Alexander Schmeding},
title = {The {Tame} {Butcher} {Group}},
journal = {Journal of Lie Theory},
pages = {1107--1144},
year = {2016},
volume = {26},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a7/}
}
TY - JOUR
AU - Geir Bogfjellmo
AU - Alexander Schmeding
TI - The Tame Butcher Group
JO - Journal of Lie Theory
PY - 2016
SP - 1107
EP - 1144
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a7/
ID - JOLT_2016_26_4_a7
ER -
%0 Journal Article
%A Geir Bogfjellmo
%A Alexander Schmeding
%T The Tame Butcher Group
%J Journal of Lie Theory
%D 2016
%P 1107-1144
%V 26
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a7/
%F JOLT_2016_26_4_a7
