Strict linear stability domain
ID: strict-linear-stability-domain
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 ; 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. Cambridge numerical analysis notes use the decay convention. Explicitly specifying the convention is essential for methods with undamped modes.
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