Abstract
The classical four-stage family of explicit sixth-order Numerov-type method is considered. We provide two kinds of interpolants: (a) a three-step interpolation based on all available data at mesh points and (b) a local interpolant (ie, two steps) that is constructed after solving scaled equations of condition. These latter equations are explained and provided here. Applying these interpolants in a set of tests, we conclude that they produce global errors of the same magnitude with the underlying method.