About: Butcher group

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Butcher group Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Science105999797, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FButcher_group&invfp=IFP_OFF&sas=SAME_AS_OFF

In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field. It was , prompted by the work of Sylvester on change of variables in differential calculus, who first noted that the derivatives of a composition of functions can be conveniently expressed in terms of rooted trees and their combinatorics.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:WikicatHopfAlgebras Band yago:Science105999797
rdfs:label	Butcher group (en)
rdfs:comment	In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field. It was , prompted by the work of Sylvester on change of variables in differential calculus, who first noted that the derivatives of a composition of functions can be conveniently expressed in terms of rooted trees and their combinatorics. (en)
foaf:depiction
dcterms:subject	Quantum field theory Combinatorics Numerical analysis Renormalization group Hopf algebras
Wikipage page ID	23338010 (xsd:integer)
Wikipage revision ID	1115667642 (xsd:integer)
Link from a Wikipage to another Wikipage	Power series Quantum field theory Rooted tree Annals of Mathematics Holomorphic function Renormalization Renormalization group Vector field Letters in Mathematical Physics Lie group Quantum field theory Counit Mathematics Gamma function Equivalence class Milnor–Moore theorem Lie algebra Faà di Bruno's formula Henri Moscovici Derivation (abstract algebra) Hopf algebra Symmetry group Automorphism John C. Butcher Minimal subtraction scheme Alain Connes Combinatorics Numerical analysis Feynman diagram Formal power series Numerical analysis Dimensional regularization Dirk Kreimer Graph theory Universal enveloping algebra Renormalization group James Joseph Sylvester Riemann sphere Augmentation ideal Laurent series Differential calculus Hopf algebras Polynomial Polynomial ring Ordinary differential equation Formal group Philosophical Magazine Rota–Baxter algebra Riemann–Hilbert problem Runge–Kutta method Séminaire Bourbaki Index theorem Comultiplication Beta-function Antipode (algebra)
Link from a Wikipage to an external page	http://www.alainconnes.org/docs/RH1.pdf%7Cdoi=10.1007/s002200050779%7Carxiv http://www.alainconnes.org/docs/RH2.pdf%7Cdoi=10.1007/PL00005547%7Carxiv http://www.alainconnes.org/docs/ncgk.pdf%7Cdoi=10.1007/s002200050499%7Carxiv http://people.math.jussieu.fr/~boutet/renormalisation.pdf https://polipapers.upv.es/index.php/AGT/article/view/2250 https://archive.org/stream/collectedmathema03cayluoft%23page/242/mode/1up%7Cjournal=
sameAs	Butcher group Butcher group Butcher group Butcher group
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cquote dbt:Harvtxt dbt:Reflist dbt:Section_link dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/Caylrich-first-trees.png?width=300
has abstract	In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-linear ordinary differential equations by the Runge–Kutta method. It arose from an algebraic formalism involving rooted trees that provides formal power series solutions of the differential equation modeling the flow of a vector field. It was , prompted by the work of Sylvester on change of variables in differential calculus, who first noted that the derivatives of a composition of functions can be conveniently expressed in terms of rooted trees and their combinatorics. pointed out that the Butcher group is the group of characters of the Hopf algebra of rooted trees that had arisen independently in their own work on renormalization in quantum field theory and Connes' work with Moscovici on local index theorems. This Hopf algebra, often called the Connes–Kreimer algebra, is essentially equivalent to the Butcher group, since its dual can be identified with the universal enveloping algebra of the Lie algebra of the Butcher group. As they commented: We regard Butcher’s work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results. (en)
gold:hypernym	Group
prov:wasDerivedFrom	wikipedia-en:Butcher_group?oldid=1115667642&ns=0
page length (characters) of wiki page	24933 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Butcher_group

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software