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Algebraic structures of B-series

Chartier, Philippe
Published in Foundations of Computational Mathematics. 2010, vol. 10, no. 4, p. 407-427
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-seriesRooted treesComposition lawSubstitution lawButcher groupHopf algebra of treesCoproductAntipodeP-seriesS-series
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CHARTIER, Philippe, HAIRER, Ernst, VILMART, Gilles. Algebraic structures of B-series. In: Foundations of Computational Mathematics, 2010, vol. 10, n° 4, p. 407-427. doi: 10.1007/s10208-010-9065-1 https://archive-ouverte.unige.ch/unige:12105

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Deposited on : 2010-10-15

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