= Amplification polynomial of a multistep method
{title2=$P_z(w)=\rho(w)-z\sigma(w)$}
= Amplification polynomial
{synonym}
Applying a <linear multistep method> to the <Dahlquist test equation> with $z=h\lambda$ produces a constant-coefficient recurrence whose modes satisfy $P_z(w)=0$. <Absolute stability> requires the resulting <roots of a polynomial> to lie in the unit disk, with unit-modulus roots simple. Thus multistep stability depends on every recurrence mode, rather than a single one-step <stability function>.
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