The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Correction of finite difference eigenvalues of periodic Sturm-Liouville problems

Alan L. Andrewa1

a1 Mathematics Department, La Trobe University, Bundoora, Victoria 3083, Australia.

Abstract

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.

(Received March 07 1988)

(Revised July 12 1988)