  We have shown previously that functionally fitted Runge-Kutta (FRK) methods
can be studied using a convenient collocation framework. Here, we extend that
framework to functionally fitted Runge-Kutta-Nystr\"om (FRKN) methods, shedding
further light on the fact that these methods can integrate a second-order
differential equation exactly if its solution is a combination of certain basis
functions, and that superconvergence can be obtained when the collocation
points satisfy some orthogonality conditions. An analysis of their stability is
also conducted.
