In this paper a class of Boundary Value Methods obtained as an extension of the Numerov's method is proposed for the numerical approximation of the eigenvalues of regular Sturm-Liouville problems subject to Dirichlet boundary conditions. It is proved that the error in the so obtained estimate of the kth eigenvalue behaves as O (k^(p + 1) h^(p - 1/2)) + O (k^(p+2) h^p), where p is the order of accuracy of the method and h is the discretization stepsize. Numerical results comparing the performances of the new matrix methods with that of the corrected Numerov's method are also reported.

Boundary Value Methods as an extension of Numerov's method for Sturm–Liouville eigenvalue estimates

ACETO, LIDIA;MAGHERINI, CECILIA;GHELARDONI, PAOLO
2009

Abstract

In this paper a class of Boundary Value Methods obtained as an extension of the Numerov's method is proposed for the numerical approximation of the eigenvalues of regular Sturm-Liouville problems subject to Dirichlet boundary conditions. It is proved that the error in the so obtained estimate of the kth eigenvalue behaves as O (k^(p + 1) h^(p - 1/2)) + O (k^(p+2) h^p), where p is the order of accuracy of the method and h is the discretization stepsize. Numerical results comparing the performances of the new matrix methods with that of the corrected Numerov's method are also reported.
Aceto, Lidia; Magherini, Cecilia; Ghelardoni, Paolo
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11568/201436
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 20
social impact