Butcher group

Known as: Butcher series, Connes-Kreimer algebra, Connes–Kreimer algebra 
In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first… (More)
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Topic mentions per year

Topic mentions per year

1974-2017
012319742017

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2016
2016
We show that without other further assumption than affine equivariance and locality, a numerical integrator has an expansion in a… (More)
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2013
2013
Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. These algebras have been… (More)
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2013
2013
Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector… (More)
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2008
2008
  • Dikanaina Harrivel
  • 2008
We show how solutions of a non–linear differential equation can be written as sum indexed by planar trees: the Butcher series… (More)
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2006
2006
  • Dikanaina HARRIVEL
  • 2006
In a first part we study the φ–field theory from the classical point of view. Using Butcher series we compute explicitly the… (More)
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2003
2003
The algebraic structure underlying non-commutative Lie-Butcher series is the free Lie algebra over ordered trees. In this paper… (More)
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Highly Cited
2003
Highly Cited
2003
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative… (More)
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2002
2002
In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge–Kutta… (More)
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2001
2001
We study a noncommutative deformation of the commutative Hopf algebra HR of rooted trees which was shown by Connes and Kreimer to… (More)
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Highly Cited
1974
Highly Cited
1974
This paper proves a theorem (“Theorem 6”) on the composition of, what we call, Butcher series. This Theorem is shown to be… (More)
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