ACCURATE COMPUTATION OF HIGHER STURM-LIOUVILLE EIGENVALUES

The computation of eigenvalues of regular Sturm-Liouville problems is considered. It is shown that a simple step-dependent linear multistep method can be used to reduce the error of the order k4h2 of the centered finite difference estimate of the k-th eigenvalue with uniform step length h, to an error of order kh2. By an appropriate minimization of the local error term of the method one can obtain even more accurate results. A comparison of the simple correction techniques of Paine, de Hoog and Anderssen and of Andrew and Paine is given. Numerical examples demonstrate the usefulness of this correction even for low values of k.