A five-stage fifth-order singly diagonally implicit Runge–Kutta–Nystr¨om method for
the integration of second order differential equations possessing an oscillatory solution,
is presented in this article. This method is P-stable, which is recommended for problems
with a theoretical solution consisting of a periodic part of moderate frequency with a high
frequency oscillation with small amplitude superimposed. It also attains an order which is
one higher than existing methods of this type. Numerical comparisons with existing methods
of this type show its clear advantage.