Algebraic Structures of B-series
نویسندگان
چکیده
منابع مشابه
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...
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By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2010
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-010-9065-1