Summary
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 orderk 4 h 2 of the centered finite difference estimate of thek-th eigenvalue with uniform step lengthh, to an error of orderkh 2. 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 ofk.
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Research Director of the National Fund for Scientific Research (N.F.W.O. Belgium)
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Vanden Berghe, G., De Meyer, H. Accurate computation of higher Sturm-Liouville eigenvalues. Numer. Math. 59, 243–254 (1991). https://doi.org/10.1007/BF01385778
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DOI: https://doi.org/10.1007/BF01385778