Approximations of Sturm-Liouville eigenvalues using boundary value methods
This paper is concerned with the numerical calculation of eigenvalues in Sturm-Liouville boundary value problems. As it is well known there are many numerical methods which provide good approximations to the first harmonics but often they are not satisfactory when the number of harmonics becomes large. The author proposes an approach to the last problem, when the boundary value problem is written in Liouville's normal form, combining an asymptotic technique of error correction of the eigenvalues [cf. \textit{A. L. Andrew} and \textit{J. W. Paine}, Numer. Math. 47, 289-300 (1985; Zbl 0554.65060)] with the discretization of the boundary value problem by means of multistep methods which use first- and second-order derivatives (sometimes referred to as Obrechkoff multistep methods). Some numerical experiments are presented to compare the efficiency of the proposed method with other similar methods based on Numerov's formula or Simpson's rule.
scientific article; zbMATH DE number 1022210