An adapted explicit hybrid method of Numerov-type for the numerical integration of perturbed oscillators

In 1971, Scheifele has designed a method for the integration of perturbed oscillators by refining the classical method of power series. In this paper, we examine how we can extend the algorithm of Scheifele for the construction of a fourth-order hybrid method without explicit first derivatives. An application to some popular test problems such as the satellite problem shows the properties of the developed algorithm.