B-series methods are exactly the affine equivariant methods

DOI10.1007/s00211-015-0753-2zbMath1364.65145arXiv1409.1019OpenAlexW3103654402MaRDI QIDQ726723

Klas Modin, Olivier Verdier, Robert I. Mclachlan, Hans Z. Munthe-Kaas

Publication date: 14 July 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1019

zbMATH Keywords

numerical integrationButcher seriesaffine equivariancesequences of maps

Mathematics Subject Classification ID

Related Items (18)

Integrators on homogeneous spaces: isotropy choice and connections ⋮ The averaged Lagrangian method ⋮ Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds ⋮ Birational maps from polarization and the preservation of measure and integrals ⋮ On expansions for nonlinear systems error estimates and convergence issues ⋮ 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 ⋮ A minimal-variable symplectic integrator on spheres ⋮ Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices ⋮ The Lie group structure of the Butcher group ⋮ The incidence comodule bialgebra of the Baez-Dolan construction ⋮ Aromatic Butcher series ⋮ Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions ⋮ 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

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