Exponentially-fitted and trigonometrically-fitted two derivative Runge-Kutta-Nystrom methods for solving y''(x) = f(x, y, y' ) - Salama, Tahani Mohamed; Senu, Norazak; Ibrahim, Zarina Bibi; Nik Long, Nik Mohd Asri (Hindawi, 2018)
Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nyström (TDRKN) methods are being constructed. Exponentially fitted and trigonometrically fitted TDRKN methods have the favorable feature that they integrate exactly second-order systems whose solutions are linear combinations of functions {exp⁡(wx),exp⁡(-wx)} and {sin⁡(wx),cos⁡(wx)} respectively, when w∈R , the frequency of the problem. The results of numerical experiments showed that the new approaches are more efficient than existing methods in the literature.