Explicit Numerov type methods with reduced number of stages

We present in this paper a new approach for the derivation of hybrid explicit Numerov type methods. The new methodology does not require the intermediate use of high accuracy interpolatory nodes, since we only need the Taylor expansion of the internal points. As a consequence, a sixth-order method is produced at a cost of only four stages per step instead of six stages needed for the methods which have appeared in the literature until now. Numerical results over some well-known problems in physics and mechanics indicate the superiority of the new method.