Revised exponentially fitted Runge-Kutta-Nystrom methods

It is the purpose of this paper to revise the well-known exponential fitting technique for the numerical solution of special second order ordinary differential equations (ODEs) $y''=f(x,y)$, with oscillatory or periodic solutions, by Runge-Kutta-Nystr\"om methods. Due to the multistage nature of these methods, the proposed technique takes into account the contribution to the error arising from the computation of the internal stages. The benefit on the accuracy of the overall numerical scheme is visible in the presented numerical evidence.