The superconsistent collocation method is based on collocation nodes which are different from those used to represent the solution. The two grids are chosen in such a way that the continuous and the discrete operators coincide on a space as larger as possible (superconsistency). There are many documented situations in which this technique provides excellent numerical results. Unfortunately very little theory has been developed. Here, a theoretical convergence analysis for the superconsistent discretization of the second derivative operator, when the representation grid is the set of Chebyshev Gauss–Lobatto nodes is carried out. To this end, a suitable quadrature formula is introduced and studied.

A Convergence Analysis for the Superconsistent Chebyshev Method / L., Fatone; Funaro, Daniele; G. J., Yoon. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 58:1(2008), pp. 88-100. [10.1016/j.apnum.2006.11.001]

A Convergence Analysis for the Superconsistent Chebyshev Method

FUNARO, Daniele;
2008

Abstract

The superconsistent collocation method is based on collocation nodes which are different from those used to represent the solution. The two grids are chosen in such a way that the continuous and the discrete operators coincide on a space as larger as possible (superconsistency). There are many documented situations in which this technique provides excellent numerical results. Unfortunately very little theory has been developed. Here, a theoretical convergence analysis for the superconsistent discretization of the second derivative operator, when the representation grid is the set of Chebyshev Gauss–Lobatto nodes is carried out. To this end, a suitable quadrature formula is introduced and studied.
58
1
88
100
A Convergence Analysis for the Superconsistent Chebyshev Method / L., Fatone; Funaro, Daniele; G. J., Yoon. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - STAMPA. - 58:1(2008), pp. 88-100. [10.1016/j.apnum.2006.11.001]
L., Fatone; Funaro, Daniele; G. J., Yoon
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/584313
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact