High order Runge–Kutta–Nyström codes for the integration of oscillatory problems Original Research Article

Most of the codes specially designed for the numerical integration of differential equations whose solution is near to a sinusoidal are capable of exactly integrating harmonic oscillators. This fact imposes the evaluation of complex functions for the computation of their coefficients which increases the computational cost when they are implemented in variable step-size. Recently, Garcı́a et al. have developed methods of Runge–Kutta–Nyström type for the numerical integration of oscillatory problems whose coefficients have a simple dependence on the step-size. In this paper, we present an embedded eighth order method of this type. The method obtained is competitive when comparing with classical and special codes.