I can't find a method on how to do this anywhere, so I'm having to ask. Thanks for any help or method you can give. I have a butcher tableau that looks like this:
\begin{array} {c|cccc} 0\\ \frac{1}{3} & \frac{1}{3}\\ \frac{2}{3} &0 &\frac{2}{3} \\ \hline & \frac{1}{4} &0 &\frac{3}{4} \end{array}
I also have proved that it is a method of order three. I now have to find the region of stability for this runge-kutta method, and sketch it. I do not understand how to do this.
P.S I have the formula:
$$ R = [\mu \; \in \; \mathbb{C} : |Q(\mu)|<1] $$
where R is the region. Happy to answer any questions you have. This is my first time doing this so not sure how much information is needed for me to give. Thank you.