Algebraic Structures of B-seriesReportar como inadecuado

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1 IPSO - Invariant Preserving SOlvers IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique 2 Section de mathématiques Genève 3 Section de Mathematiques Lausanne

Abstract : B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight into modified differential equations of backward error analysis. These two laws give rise to algebraic structures groups and Hopf algebras of trees that have recently received much attention also in the non-numerical literature. This article emphasizes these algebraic structures and presents interesting relationships among them.

Keywords : B-series Rooted trees Composition law Substitution law Butcher group Hopf algebra of trees Coproduct Antipode P-series S-series

Autor: Philippe Chartier - Ernst Hairer - Gilles Vilmart -



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