Approximations of Sturm-Liouville eigenvalues using Boundary Value Methods

It is well known that the algebraic approximations to eigenvalues of a Sturm-Liouville problem by the central difference and Numerov's schemes provide only a few estimates restricted to the first element of the eigenvalue sequence. A correction technique, used first by Paine et al. (1981) for the central difference scheme and then by Andrew and Paine (1985) for Numerov's method, improves the results, giving acceptable estimates for a larger number of eigenvalues. In this paper some linear multistep methods, called Boundary Value Methods, are proposed for discretizing a Sturm-Liouville problem and the correction technique of Andrew-Paine and Paine et al. is extended to these new methods.