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B-series methods are exactly the affine equivariant methods

Författare och institution:
R.I. McLachlan (-); Klas Modin (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); H. Munthe-Kaas (-); O. Verdier (-)
Publicerad i:
Numerische Mathematik, 133 ( 3 ) s. 599-622
ISSN:
0029-599X
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2016
Språk:
engelska
Fulltextlänk:
Sammanfattning (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 spaces has a B-series expansion if and only if it is affine equivariant, meaning it respects all affine maps between affine spaces.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Geometri
NATURVETENSKAP ->
Matematik ->
Beräkningsmatematik
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
221569
Posten skapad:
2015-09-01 08:36
Posten ändrad:
2016-06-22 10:07

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