Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10208-010-9065-1 | Foundations of Computational Mathematics |
Keywords | Field | DocType |
B-series,Rooted trees,Composition law,Substitution law,Butcher group,Hopf algebra of trees,Coproduct,Antipode,P-series,S-series,65L06,65P10,37C10,16W30 | Differential equation,Mathematical optimization,Dimension of an algebraic variety,Algebra,Ordinary differential equation,Mathematical analysis,Differential algebraic geometry,Algebraic cycle,Differential algebraic equation,Real algebraic geometry,Hopf algebra,Mathematics | Journal |
Volume | Issue | ISSN |
10 | 4 | 1615-3375 |
Citations | PageRank | References |
14 | 1.26 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| P. Chartier | 1 | 144 | 29.70 |
| Ernst Hairer | 2 | 237 | 51.27 |
| Gilles Vilmart | 3 | 65 | 11.76 |