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

Authors:
L. Aceto;P. Ghelardoni;C. Magherini
Affiliations:
Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, Italy;Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, Italy;Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, Italy
Venue:
Applied Numerical Mathematics
Year:
2009

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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^+^1h^p^-^1^2)+O(k^p^+^2h^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.