Exponentially-fitted Numerov methods

The error in the estimate of the kth eigenvalue of a regular Sturm–Liouville problem obtained by Numerov's method with mesh length h   is O(k6h4)O(k6h4). It is shown that the error can be reduced to O(k3h4)O(k3h4) by using one of the three versions of the exponentially-fitted Numerov method. Numerical examples demonstrate the usefulness of this approach even for low values of k.