A Runge-Kutta-Nystrom Method for Delay Differential Equations

Let consider the following boundary value problem for second order delay differential systems: 1$$ \begin{gathered} y''\left( t \right) = f\left( {t,y\left( t \right),y'\left( t \right),y\left( {t - \tau \left( t \right)} \right),y'\left( {t - \sigma \left( t \right)} \right)} \right) {t_o} \leqslant t \leqslant b \hfill \\ y'\left( t \right) = \phi \left( t \right) t \leqslant {t_o} \hfill \\ y'\left( t \right) = \phi '\left( t \right) t < {t_o} \hfill \\ y\left( b \right) = {y_b} \hfill \\ \end{gathered} $$ y: IR → IRm, f: [ t_o,b ]×IR4m → IR and τ(t), σ(t)>0.