The steps involve with the aid of maple software will be appreciated.
You don't plot stab region for the so-called trig fitted with boundary locus. But if you insist on the boundary locus, then you the could present some plots for some values of frequency value. It also depeneds on the problem type. For frequency dependent methods what matters is the phase analysis, and the stability region is very complicated for Runge-Kutta methods. Idea is to compare \omega, fitting frequency and \lambda test frequency.
Apply the method to the test frequency do your normal substitution. Put in form y_n+k=R y_n. The R is piloted for \nu against \omega.
The second comment cut. I actually meant the eigenvalues of R bounded by 1 should be plotted with\nu against \omega.
@Ehigie. Thank you sir you comments are useful I have started working on it. I will send an update to you via email
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