Correction of finite difference eigenvalues of periodic Sturm-Liouville problems

Computation of eigenvalues of regular Sturm-Liouville problems with periodic or semiperiodic boundary conditions is considered. A simple asymptotic correction technique of Paine, de Hoog and Anderssen is shown to reduce the error in the centred finite difference estimate of the kth eigenvalue obtained with uniform step length h from O(k4h2) to O(kh2). Possible extensions of the results are suggested and the relative advantages of the method are discussed.