= Runge-Kutta stage
{c}
{title2=$k_i=f(t_n+c_i h,Y_i)$}
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, $Y_i=y_n+h\sum_ja_{ij}k_j$. 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.
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