Starting algorithms for low stage order RKN methods

When second order differential equations are solved with Runge-Kutta-Nystrِm methods, the computational effort is dominated by the cost of solving the nonlinear system. That is why it is important to have good starting values to begin the iterations. In this paper we consider a type of starting algorithms without additional computational cost. We study the general order conditions and the maximum order achieved when the Runge-Kutta-Nystrِm method satisfies some simplifying assumptions.