Collocation tableau row-sum identity
= Collocation tableau row-sum identity
{title2=$A\mathbf1=c$}
For a <collocation Runge-Kutta method>, $a_{ij}=\int_0^{c_i}\ell_j(t)dt$, where the <Lagrange interpolation> basis obeys $\sum_j\ell_j=1$. Hence each row sum is its collocation node. Failure of this identity disproves a claimed collocation tableau with those nodes. The identity alone is necessary rather than sufficient: the individual integrated basis coefficients must also agree.