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.
2006
44
1954
1973
F. MAZZIA; A. SESTINI; D. TRIGIANTE
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/256836
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