Exponentially-fitted Numerov methods

The error in the estimate of the kth eigenvalue of a regular Sturm–Liouville problem obtained by Numerovʹs method with mesh length h is O ( k 6 h 4 ) . It is shown that the error can be reduced to O ( k 3 h 4 ) 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.