The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Generation of a section of conjugation classes and Lyndon word tree of limited length
Theoretical Computer Science
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical integration of differential equations on homogeneous manifolds
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
High order Runge-Kutta methods on manifolds
proceedings of the on Numerical analysis of hamiltonian differential equations
Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
SIAM Journal on Numerical Analysis
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The algebraic structure underlying non-commutative Lie-Butcher series is the free Lie algebra over ordered trees. In this paper we present a characterization of this algebra in terms of balanced Lyndon words over a binary alphabet. This yields a systematic manner of enumerating terms in non-commutative Lie-Butcher series.