Collocation Runge-Kutta method
= Collocation Runge-Kutta method
Given distinct nodes $c_i$, a collocation Runge-Kutta method uses the Lagrange basis $\ell_j$ with $a_{ij}=\int_0^{c_i}\ell_j(\tau)d\tau$ and $b_j=\int_0^1\ell_j(\tau)d\tau$. Its stages enforce the differential equation at the collocation nodes.
This applies the <collocation method> to the time-step polynomial of an <ordinary differential equation>.