Article: B-series methods are exactly the local, affine equivariant methods
Authors: Robert I. McLachlan, Klas Modin, Hans Munthe-Kaas, Olivier Verdier
Journal: Submitted.
Abstract: Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined in all dimensions, so they correspond to sequences of maps — one map for each dimension. A long-standing problem has been to characterise those sequences of maps that arise from B-series. This problem is solved here: we prove that a sequence of smooth maps between vector fields on affine linear spaces has a B-series expansion if and only if it is local and affine equivariant, meaning it respects all affine linear maps between affine spaces.
Hindsight notes: None yet.
3 Sep 2014