An adapted explicit hybrid four-step method for the numerical solution of perturbed oscillators

In this paper, the construction of an adapted explicit hybrid four-step method for the numerical integration of perturbed oscillators is investigated. This four-step method is based on the algorithm of Scheifele which is obtained by refining the classical method of power series. The local truncation error, phase properties and linear stability of the new method are analyzed. Numerical experiments are reported to show the high accuracy and efficiency of the new method when it is compared with some high-quality methods recently proposed in the literature.