Look at the ODE
$$ y'=\begin{pmatrix} 0 & 1\\ -1 & 0 \end{pmatrix} y$$
Let $y_i$ be the the numerical solution calculated by Heun's method. For which $h>0$ is $\|y_{i+1}\|_2 \leq \|y_i\|_2$?
I know that $R(z)=1+z+\frac{z^2}{2}$ ($z=\lambda h$) is the stability function of the scalar DE $y'=\lambda y$ and $|y_{i+1}|=|R(z)||y_i|$ in the scalar case. Any hints for this system?