Algebraic Structures of B-series

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Algebraic Structures of B-series
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.
Philippe Chartier, Ernst Hairer, Gilles Vilmart
Added 25 Jan 2011
Updated 25 Jan 2011
Type Journal
Year 2010
Where FOCM
Authors Philippe Chartier, Ernst Hairer, Gilles Vilmart
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