I am working on a analysis of different numerical methods and I am trying to plot the stability region of a numerical method.
For instance if we look at the absolute stability requirements for the explicit euler method we get the condition
which yields the region of absolute stability in the complex plain shown in the image below
Now for this exact method the stability is a perfect circle and I could find a way to simply plot a circle with a radius of 1 and a center in (0,-1), but for most cases it isnt a perfect circle but rather a skewed one.
I tried making the circle through a function handle with the variable z where I plotted it from -2<=z<=0 but it didnt turn out as I hoped.
Is there anyone that can help me in forming an function, or something else, from the inequality and similiar inequalities?