= Newton-Cotes multistep methods attaining the first Dahlquist barrier
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{title2=$Y_{n+s}-Y_n=h\sum_{j=0}^sw_jf_{n+j}$}
Using <Newton-Cotes closed quadrature> for the integrated derivative yields the displayed <linear multistep method>. Its first <characteristic polynomial> is $\rho(z)=z^s-1$, whose unit-circle roots are all simple, proving <zero-stability>. Quadrature exactness gives order $s+1$ for odd $s$ and at least $s+2$ for even $s$. The <first Dahlquist barrier> gives equality, while the <Dahlquist equivalence theorem> gives convergence with consistent starts. These are finite-time convergence statements, not claims of <A-stability>.
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