B-Spline Linear Multistep Methods and their Continuous Extensions

Authors:
Francesca Mazzia;Alessandra Sestini;Donato Trigiante
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2006

Citing 0
Cited 7

The stability problem for linear multistep methods: Old and new results

Journal of Computational and Applied Mathematics
The continuous extension of the B-spline linear multistep methods for BVPs on non-uniform meshes

Applied Numerical Mathematics
On the relations between B2V Ms and Runge-Kutta collocation methods

Journal of Computational and Applied Mathematics
Quadrature formulas descending from BS Hermite spline quasi-interpolation

Journal of Computational and Applied Mathematics
PGSCM: A family of P-stable Boundary Value Methods for second-order initial value problems

Journal of Computational and Applied Mathematics
Linear/linear rational spline collocation for linear boundary value problems

Journal of Computational and Applied Mathematics
Delay-dependent stability analysis of symmetric boundary value methods for linear delay integro-differential equations

Numerical Algorithms

Quantified Score

Hi-index	0.01

Visualization

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.