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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2016

2016

- Hans Z. Munthe-Kaas, Olivier Verdier
- Foundations of Computational Mathematics
- 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

- Hans Z. Munthe-Kaas, Alexander Lundervold
- Foundations of Computational Mathematics
- 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

- Andreas Sandvin, Eirik Keilegavlen, Jan M. Nordbotten
- J. Comput. Physics
- 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

- Hans Z. Munthe-Kaas, Stein Krogstad
- Future Generation Comp. Syst.
- 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

- Alain Connes, Dirk Kreimer
- 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

- Kevin Burrage, Tianhai Tian
- SIAM J. Numerical Analysis
- 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

- Ernst Hairer, Gerhard Wanner
- Computing
- 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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