A new eight-order symmetric two-step multiderivative method for the numerical solution of second-order IVPs with oscillating solutions

In this paper, we introduce a class of new two-step multiderivative methods for the numerical solution of second-order initial value problems. We generate a two-step, symmetric, multiderivative method of order 8. We also perform a periodicity analysis. In addition, we determine their periodicity regions. Finally, we compare the new methods to the corresponding classical ones and other known methods from the literature, where we show the high efficiency of the new methods.