Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nystrom Methods for Solving y"(x) = f (x, y, y′)

Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nystrom (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 is an element of 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.