= Strict linear stability domain
{title2=$\mathcal D_{\rm decay}=\{z:y_n\to0\}$}
The strict decay convention for a <linear stability domain> demands that every numerical mode tends to zero on the <Dahlquist test equation>. For a one-step <stability function> it requires $|R(z)|<1$; for a <multistep method> it requires every <amplification root> to have <modulus> below one. This differs from a boundedness convention that allows simple <unit-circle roots>, and from mesh-uniform finite-time <numerical stability>. https://www.damtp.cam.ac.uk/user/na/PartIB/Lect10.pdf[Cambridge numerical analysis notes] use the decay convention. Explicitly specifying the convention is essential for methods with undamped modes.
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