A numerical integrator for ẋ=f(x) is called stable if, when applied to the 1D Dahlquist test equation ẋ=λ x,λ∈ℂ with fixed timestep h>0, the numerical solution remains bounded as the number of steps tends to infinity. It is well known that no explicit integrator may remain stable beyond certain limits in λ. Furthermore, these stability limits are only tight for certain specific integrators (different in each case), which may then be called `optimally stable'. Such optimal stability results are t...