We consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.

The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results

MASET, STEFANO
2015

Abstract

We consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.
Pubblicato
http://epubs.siam.org/loi/sjnaam
File in questo prodotto:
File Dimensione Formato  
maset2015.pdf

non disponibili

Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 246.93 kB
Formato Adobe PDF
246.93 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
2855423_maset2015-PostPrint.pdf

accesso aperto

Descrizione: Post Print VQR3
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 855.52 kB
Formato Adobe PDF
855.52 kB Adobe PDF Visualizza/Apri

I documenti in IRIS 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/11368/2855423
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact