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

L. Aceto, P. Ghelardoni, C. Magherini

Research output: Contribution to journalArticlepeer-review

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 (kp + 1 hp - frac(1, 2)) + O (kp + 2 hp), 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.

Original languageEnglish
Pages (from-to)1644-1656
Number of pages13
JournalApplied Numerical Mathematics
Volume59
Issue number7
DOIs
Publication statusPublished - Jul 2009
Externally publishedYes

Keywords

  • Boundary Value Methods
  • Eigenvalues
  • Sturm-Liouville problems

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