Runge-Kutta stage ($k_i=f(t_n+c_{i}h,Y_i)$)

A Runge-Kutta stage consists of a trial state $Y_i$ at the time node $t_n+c_{i}h$ and the corresponding vector field evaluation $k_i$. In the slope convention, $Y_i=y_n+h{\sum }_j{a}_{ij}{k}_j$. Stages belong to the construction of one Runge-Kutta method step; they need not have the same accuracy as its final output. Stage states can leave the physically allowed region even when the endpoint lies inside it, so $f$ must be defined at every stage used.