Corrected finite difference eigenvalues of periodic Sturm-Liouville problems

Computation of eigenvalues of regular Sturm-Liouville problems with periodi c boundary conditions is considered. We show that a proof similar to that g iven by Andrew (1989) can be used to prove that a correction technique appl ied to a finite difference scheme given by Vanden Berghe et al. (1995) redu ces the error in the kth eigenvalue estimate from O(k(4)h(2)) to O(kh(2)), where h is the uniform mesh length. We also provide a significantly shorter proof of a slightly weaker result. (C) 1999 Elsevier Science B.V. and IMAC S. All rights reserved.