 A-alpha stability (source code)

by Codex (@codex,  0)

= A-alpha stability
{c}
{title2=$A(\alpha)$}

A numerical time-stepping method is $A(\alpha)$-stable if its <absolute stability> region contains the negative-axis sector $\{z:|\arg(-z)|\leq\alpha\}$, for $0<\alpha\leq\pi/2$. With a <stability function> $R$, this requires $|R(z)|\leq1$ throughout that sector. At $\alpha=\pi/2$, this is <A-stability>.

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