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.
|Autori:||ACETO L; MAGHERINI C; GHELARDONI P|
|Titolo:||Boundary Value Methods as an extension of Numerov's method for Sturm–Liouville eigenvalue estimates|
|Anno del prodotto:||2009|
|Digital Object Identifier (DOI):||10.1016/j.apnum.2008.11.005|
|Appare nelle tipologie:||1.1 Articolo in rivista|