J. Álvarez and J.
An improved class of generalized
Runge-Kutta-Nyström methods for special second order differential
equations, Commun. Nonlinear
Sci. Numer. Simul., 9 (2003), pp. 217-227.
We propose a new family
of explicit methods of order four with two evaluations per step, for the
numerical integration of special second order differential equations given
by y''=f(y) . These two-stage formulas can be seen as a generalization
of the explicit two-stage Runge-Kutta-Nyström methods, providing better
order and stability results. We will show that it is possible to obtain
methods that are more efficient than the classical Runge-Kutta-Nyström
one-step methods with the same number of evaluations per step, specially
when highly oscillatory problems are considered. Some numerical experiments
are discussed in order to show the good performance of the new schemes.
AMS(MOS) subject classification:
65L05, 65L06, 65L20
Preprint file as PDF nystro.pdf