Correction of finite difference eigenvalues of periodic Sturm-Liouville problems

1 January 1989

journal article
research article
Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Vol. 30 (4) , 460-469
https://doi.org/10.1017/s0334270000006391

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.

Keywords

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