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- Butcher_group abstract "In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional 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 Cayley (1857), 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. Connes & Kreimer (1999) 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:".
- Butcher_group thumbnail Caylrich-first-trees.png?width=300.
- Butcher_group wikiPageExternalLink renormalisation.pdf.
- Butcher_group wikiPageExternalLink journal-03.pdf.
- Butcher_group wikiPageID "23338010".
- Butcher_group wikiPageRevisionID "578116672".
- Butcher_group hasPhotoCollection Butcher_group.
- Butcher_group subject Category:Combinatorics.
- Butcher_group subject Category:Hopf_algebras.
- Butcher_group subject Category:Numerical_analysis.
- Butcher_group subject Category:Quantum_field_theory.
- Butcher_group subject Category:Renormalization_group.
- Butcher_group type Abstraction100002137.
- Butcher_group type Algebra106012726.
- Butcher_group type Cognition100023271.
- Butcher_group type Content105809192.
- Butcher_group type Discipline105996646.
- Butcher_group type HopfAlgebras.
- Butcher_group type KnowledgeDomain105999266.
- Butcher_group type Mathematics106000644.
- Butcher_group type PsychologicalFeature100023100.
- Butcher_group type PureMathematics106003682.
- Butcher_group type Science105999797.
- Butcher_group comment "In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional 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.".
- Butcher_group label "Butcher group".
- Butcher_group sameAs m.06w5q7x.
- Butcher_group sameAs Q5002457.
- Butcher_group sameAs Q5002457.
- Butcher_group sameAs Butcher_group.
- Butcher_group wasDerivedFrom Butcher_group?oldid=578116672.
- Butcher_group depiction Caylrich-first-trees.png.
- Butcher_group isPrimaryTopicOf Butcher_group.