A-alpha stability ($A(\alpha )$)

A numerical time-stepping method is $A(\alpha )$-stable if its absolute stability region contains the negative-axis sector $\{z:|\arg (-z)|\le \alpha \}$, for $0<\alpha \le \pi /2$. With a stability function $R$, this requires $|R(z)|\le 1$ throughout that sector. At $\alpha =\pi /2$, this is A-stability.