Summary: A modified phase-fitted Runge-Kutta method (i.e., a method with phase-lag of order infinity) for the numerical solution of periodic initial-value problems is constructed. This new modified method is based on the Runge-Kutta fifth algebraic order method of J. R. Dormand
and P. J. Prince
[J. Comput. Appl. Math. 6, 19–26 (1980; Zbl 0448.65045
)]. The numerical results indicate that this new method is more efficient for the numerical solution of periodic initial-value problems than the well known Runge-Kutta method of Dormand and Prince [loc. cit.] with algebraic order five.