In this paper, starting from a sequence of results which can be traced back to I. J. Schoenberg, we analyze a class of spline collocation methods for the numerical solution of ordinary differential equations (ODEs) with collocation points coinciding with the knots. Such collocation methods are naturally associated to a special class of linear multistep methods, here called B-spline (BS) methods, which are able to generate the spline values at the knots. We prove that, provided the additional conditions are appropriately chosen, such methods are all convergent and A-stable. The convergence property of the BS methods is naturally inherited by the related spline extensions, which, by the way, are easily and safely computable using their B-spline representation.

B-spline multistep methods and their continuous extensions / F. MAZZIA; A. SESTINI; D. TRIGIANTE. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 44(2006), pp. 1954-1973. [10.1137/040614748]

B-spline multistep methods and their continuous extensions

SESTINI, ALESSANDRA;TRIGIANTE, DONATO
2006

Abstract

In this paper, starting from a sequence of results which can be traced back to I. J. Schoenberg, we analyze a class of spline collocation methods for the numerical solution of ordinary differential equations (ODEs) with collocation points coinciding with the knots. Such collocation methods are naturally associated to a special class of linear multistep methods, here called B-spline (BS) methods, which are able to generate the spline values at the knots. We prove that, provided the additional conditions are appropriately chosen, such methods are all convergent and A-stable. The convergence property of the BS methods is naturally inherited by the related spline extensions, which, by the way, are easily and safely computable using their B-spline representation.
44
1954
1973
F. MAZZIA; A. SESTINI; D. TRIGIANTE
File in questo prodotto:
File Dimensione Formato  
siam.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: DRM non definito
Dimensione 236.36 kB
Formato Adobe PDF
236.36 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/256836
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 38
  • ???jsp.display-item.citation.isi??? 35
social impact