The Lie group structure of the Butcher group

DOI10.1007/s10208-015-9285-5zbMath1366.22010arXiv1410.4761OpenAlexW3106337495WikidataQ115385137 ScholiaQ115385137MaRDI QIDQ525601

Alexander Schmeding, Geir Bogfjellmo

Publication date: 5 May 2017

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.4761

zbMATH Keywords

Hopf algebra of rooted treessymplectic methodsinfinite-dimensional Lie groupButcher groupregularity of Lie groups

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Real-analytic and Nash manifolds (58A07) Hopf algebras and their applications (16T05)

Related Items

Computing normal forms and formal invariants of dynamical systems by means of word series ⋮ Word series for dynamical systems and their numerical integrators ⋮ Lie groups of controlled characters of combinatorial Hopf algebras ⋮ Unnamed Item ⋮ Rooted Tree Graphs and the Butcher Group: Combinatorics of Elementary Perturbation Theory ⋮ Character groups of Hopf algebras as infinite-dimensional Lie groups ⋮ Algebraic structure of aromatic B-series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Character groups of Hopf algebras as infinite-dimensional Lie groups
• Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case
• B-series methods are exactly the affine equivariant methods
• Instructive examples of smooth, complex differentiable and complex analytic mappings into locally convex spaces
• Towards a Lie theory of locally convex groups
• Differential calculus in locally convex spaces
• Hopf algebras, renormalization and noncommutative geometry
• Canonical \(B\)-series
• The life-span of backward error analysis for numerical integrators
• Trees, renormalization and differential equations.
• Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
• Algebraic structures of B-series
• Differentiable mappings on products with different degrees of differentiability in the two factors
• A Lie theoretic approach to renormalization
• Applications différentiables et variétés différentiables de dimension infinie
• The structure of the ladder insertion-elimination Lie algebra
• Locally Unbounded Topological Fields and Box Topologies on Products of Vector Spaces†
• Geometric Numerical Integration
• An Algebraic Theory of Integration Methods
• BOX TOPOLOGIES

This page was built for publication: The Lie group structure of the Butcher group