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Journal Articles Foundations of Computational Mathematics Year : 2010

Algebraic Structures of B-series

Philippe Chartier
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Ernst Hairer
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Gilles Vilmart
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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.
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inria-00598369 , version 1 (06-06-2011)



Philippe Chartier, Ernst Hairer, Gilles Vilmart. Algebraic Structures of B-series. Foundations of Computational Mathematics, 2010, 10 (4), pp.407-420. ⟨10.1007/s10208-010-9065-1⟩. ⟨inria-00598369⟩
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