B-series Methods Are Exactly the Affine Equivariant Methods
Robert I. McLachlan, Klas Modin, Hans Z. Munthe-Kaas, Olivier Verdier
Numerische Mathematik2016
Abstract
We prove that B-series methods are precisely the numerical integrators that are equivariant under affine transformations. This characterization theorem provides a fundamental understanding of which numerical methods can be analyzed using B-series, connecting geometric invariance with algebraic structure.
Cite this publication
@article{robertimclachlan2016bseries,
author = {Robert I. McLachlan and Klas Modin and Hans Z. Munthe-Kaas and Olivier Verdier},
title = {B-series Methods Are Exactly the Affine Equivariant Methods},
journal = {Numerische Mathematik},
year = {2016},
doi = {10.1007/s00211-015-0753-2},
eprint = {1409.1019},
archivePrefix = {arXiv}
}