Hey,

I'm trying to determine the region of stability for the Heun method and whether it is A stable. I've looked at the examples on wiki here Stiff equation - Wikipedia, the free encyclopedia and Runge here. By plugging in the test equation y' = zy where k is complex I've simplified the Heun algorithm from

$\displaystyle $$y_{n+1} = y_n + 0.5\cdot h\bigl(f(t_n, y_n) + f(t_{n+1},y_n + 0.5\cdot h\cdot f(t_n, y_n)\bigr)$$$

then when I insert $\displaystyle $y' = zy$ for $f(t,y)$$, my result simplifies to

$\displaystyle $$ y_{n+1} = (0.25\cdot h^2 \cdot z^2 + hz + 1)y_n $$$

to judge from the wiki article, the stability region is then the area described by

$\displaystyle $$\\{z \in \mathbb C \mid 0.25h^2z^2 + hz + 1 < 1\\}$$$

Am I on the right path at all? How does this relate to A stability? Appreciate any help.