Accurate numerical approximations to initial value problems with periodical solutions (Q2366311)

This paper is concerned with the numerical solution of initial value problems for ordinary differential equations with periodic solutions by means of explicit Runge-Kutta (RK) methods. The methods proposed by the authors are RK of Fehlberg type (NASA, Technical Report 315 (1969)) with order four (five stages) and order five (six stages), where the free parameters of the methods have been chosen to make the phase-lag and the dissipative orders as large as possible. Finally, some numerical examples are presented to show that the new methods perform better than other RK methods for periodic problems proposed by \textit{P. J. Van der Houwen} and \textit{B. P. Sommeijer} [SIAM J. Numer. Anal. 24, 595-617 (1987; Zbl 0624.65058)].