Aromatic Butcher series

DOI10.1007/s10208-015-9245-0zbMath1368.65113arXiv1308.5824OpenAlexW1968747035MaRDI QIDQ5963083

Hans Z. Munthe-Kaas, Olivier Verdier

Publication date: 4 March 2016

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

Full work available at URL: https://arxiv.org/abs/1308.5824

zbMATH Keywords

Runge-Kutta methodsButcher seriesaromatic seriesaromatic treeB-seriesnumerical integrator

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Dynamics induced by flows and semiflows (37C10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items

Integrators on homogeneous spaces: isotropy choice and connections ⋮ Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds ⋮ Functional equivariance and conservation laws in numerical integration ⋮ The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators ⋮ The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators ⋮ B-series methods are exactly the affine equivariant methods ⋮ Algebraic structure of aromatic B-series ⋮ Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs ⋮ The universal pre-Lie-Rinehart algebras of aromatic trees ⋮ Constructing general rough differential equations through flow approximations

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• B-series methods are exactly the affine equivariant methods
• Time-periodic solutions of the Burgers equation
• B-series methods cannot be volume-preserving
• A linear-time algorithm for finding a minimum spanning pseudoforest
• Set theory. With an introduction to descriptive set theory. Translation of the original Polish edition. 2nd, completely revised ed
• Invariant tensors and graphs
• Preserving first integrals and volume forms of additively split systems
• Solving Ordinary Differential Equations II
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• An Algebraic Theory of Integration Methods