Generalization of the Stِrmer method for perturbed oscillators without explicit first derivatives

In this work we construct a numerical method specially designed for perturbed oscillators without explicit first derivatives. The new method, which generalizes the classical Störmer and Cowell codes for second-order equations, is useful when the calculation of the first derivative is not needed because this derivative is not computed. Some numerical examples of the artificial satellite problem show the good behaviour of the methods when they compete against classical multistep and Runge–Kutta–Nyström codes.