The Top Order Methods are a class of linear multistep schemes to be used as Boundary Value Methods and with the feature of having maximal order (2k if k is the number of steps). This often implies that accurate numerical approximations of general BVPs can be produced just using the 3-step TOM. In this work, we consider two different possibilities for defining a continuous approximation of the numerical solution, the standard C-1 cubic spline collocating the differential equation at the knots and a C2k-1 spline of degree 2k. The computation of the B-spline coefficients of this higher degree spline requires the solution of N + 2k banded linear systems of size 4k x 4k. The resulting B-spline function is convergent of order 2k to the exact solution of the continuous BVPs.

High Order Continuous Approximation for the Top Order Methods / F. MAZZIA; A. SESTINI; D. TRIGIANTE. - STAMPA. - 936:(2007), pp. 611-613. (Intervento presentato al convegno ICNAAM 2007 tenutosi a Corfù, Grecia nel 16--20 Settembre 2007) [10.1063/1.2790221].

High Order Continuous Approximation for the Top Order Methods

SESTINI, ALESSANDRA;TRIGIANTE, DONATO
2007

Abstract

The Top Order Methods are a class of linear multistep schemes to be used as Boundary Value Methods and with the feature of having maximal order (2k if k is the number of steps). This often implies that accurate numerical approximations of general BVPs can be produced just using the 3-step TOM. In this work, we consider two different possibilities for defining a continuous approximation of the numerical solution, the standard C-1 cubic spline collocating the differential equation at the knots and a C2k-1 spline of degree 2k. The computation of the B-spline coefficients of this higher degree spline requires the solution of N + 2k banded linear systems of size 4k x 4k. The resulting B-spline function is convergent of order 2k to the exact solution of the continuous BVPs.
2007
Proceedings ICNAAM 2007
ICNAAM 2007
Corfù, Grecia
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/2158/261505
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