I'm trying to determine the stability region of the Heun method for ODEs by using the equation $y' = ky$, where $k$ is a complex number, based on the method described here.
If the Heun method is:
$y_{n+1} = y_n + 0.5\cdot h\bigl(f(t_n, y_n) + f(t_{n+1},y_n + 0.5\cdot h\cdot f(t_n, y_n)\bigr)$
then when I insert $y' = zy$ for $f(t,y)$, my result simplifies to
$ y_{n+1} = (0.25\cdot h^2 \cdot z^2 + hz + 1)y_n $
to judge from the wiki article, the stability region is then the area described by
$\\{z \in \mathbb C \mid 0.25h^2z^2 + hz + 1 < 1\\}$
Am I doing this right? What would such a region look like? Can someone help me get the intuition for this? And then I guess the method is A-stable if that region includes wherever $\Re < 0$?