In order to plot the region of absolute stability for Runge-Kutta methods, we notice that for the method
\[y_{n+1} = p(h\lambda)y_{n}\]
to be stable, we require
\[|p(\kappa)| < 1\]
For some polynomial $p(h\lambda)$.  For Runge-Kutta methods, the polynomial $p(\kappa)$ is defined as
\[p(\kappa) = \sum_{i=0}^{k} \frac{1}{i!} \kappa^{i}\]
Where $\kappa = h\lambda$ is complex and $k$ is the stage of the method.  For $k=4$, we get
\[p(\kappa) = 1 + \kappa + \frac{1}{2}\kappa^{2} + \frac{1}{6}\kappa^{3} + \frac{1}{24}\kappa^{4}\]
We have written a routine in Python that scans through the complex plane and plots a point where $|p(\kappa)| < 1$.  (Code available on request.)  The routine produces this figure
\begin{center}
\includegraphics[height=9cm,width=9cm]{abs_stab}
\end{center}
