Abstract
The computation of eigenvalues of regular Sturm-Liouville problems is considered. It is shown that a modified Numerov method can be used to reduce the error of the order k 6 h 4 of the classical Numerov method of the kth eigenvalue with uniform step length h, to an error of order k 3 h 4 . 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 Andrew and Paine to Numerov's method is given. Numerical examples demonstrate the usefulness of the present approach even for low values of k.
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