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B-series methods are exactly the affine equivariant methods

R.I. McLachlan ; Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; H. Munthe-Kaas ; O. Verdier
Numerische Mathematik (0029-599X). Vol. 133 (2016), 3, p. 599-622.
[Artikel, refereegranskad vetenskaplig]

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 spaces has a B-series expansion if and only if it is affine equivariant, meaning it respects all affine maps between affine spaces.

Denna post skapades 2015-09-01. Senast ändrad 2016-06-22.
CPL Pubid: 221569


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