Invariant Connections, Lie Algebra Actions, and Foundations of Numerical Integration on Manifolds

DOI10.1137/19M1252879zbMath1433.53035arXiv1903.10056WikidataQ114615466 ScholiaQ114615466MaRDI QIDQ5215534

Hans Z. Munthe-Kaas, Olivier Verdier, Ari Stern

Publication date: 12 February 2020

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.10056

zbMATH Keywords

Lie algebroidsconnectionspre-Lie algebrasLie-Butcher seriespost-Lie algebrasnumerical integration on manifolds

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Connections (general theory) (53C05) Numerical integration (65D30) Nonassociative algebras satisfying other identities (17A30)

Related Items (4)

Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods ⋮ Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion ⋮ Integration and geometrization of Rota-Baxter Lie algebras ⋮ The universal pre-Lie-Rinehart algebras of aromatic trees

Cites Work

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• On post-Lie algebras, Lie-Butcher series and moving frames
• Homology of generalized partition posets
• On the Hopf algebraic structure of Lie group integrators.
• Chronological algebras and nonstationary vector fields
• On the Butcher group and general multi-value methods
• High order Runge-Kutta methods on manifolds
• Lie algebroids and Poisson-Nijenhuis structures
• Runge-Kutta methods on Lie groups
• Integrability of Lie brackets
• Quasi-derivations and QD-algebroids
• Lie algebroids, holonomy and characteristic classes
• Lie-Butcher theory for Runge-Kutta methods
• The cohomology structure of an associative ring
• Symmetric spaces and Lie triple systems in numerical analysis of differential equations
• Pontryagin Maximum Principle on Almost Lie Algebroids
• Representations up to homotopy of Lie algebroids
• Geometric Numerical Integration
• Geometric structures as deformed infinitesimal symmetries
• Coefficients for the study of Runge-Kutta integration processes
• An Algebraic Theory of Integration Methods
• Power-associative rings
• Lie and Jordan Triple Systems
• Invariant Affine Connections on Homogeneous Spaces

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