Bug for Nonconnected Stability Regions

[Steven-Roberts]

The stab_region function only returns the first contour detected by contourc:

analysis-utilities/RungeKutta/stab_region.m

Line 56 in 85d730a

c = contourc(x,y,R,[1+eps 1+eps]);

If a method has multiple disconnected regions of stability like https://github.com/LLNL/sundials/blob/54d9c4a6a73ba52c8adb010f1ed0ec66b169c7dc/doc/shared/figs/arkode/sofroniou_spaletta_erk_stab_region.png
this code would only show one region and leave out the others. I'm not sure if stability plots in the SUNDIALS docs are affected. A simple fix is to directly call contour with the x-y grid and stability functions values.

[drreynolds]

Given that it's essentially impossible to leverage separate stability "islands" in an adaptive solver, I don't see any issues with displaying only the main region. However, if you'd like then I would be fine with a PR to update the script in this utilities repository, and then regenerating the stability region plots for the ARKODE documentation.

[Steven-Roberts]

I agree that the islands are not particularly useful, but it can display one island and not the primary region. I'll put this as a low priority item on my todo list