  The perturbative stability of catenoidal soap films formed between parallel,
equal radii, coaxial rings is studied using analytical and semi-analytical
methods. Using a theorem on the nature of eigenvalues for a class of
Sturm--Liouville operators, we show that for the given boundary conditions,
azimuthally asymmetric perturbations are stable, while symmetric perturbations
lead to an instability--a result demonstrated in Ben Amar et. al [7] using
numerics and experiment. Further, we show how to obtain the lowest real
eigenvalue of perturbations, using the semi-analytical Asymptotic Iteration
Method (AIM). Conclusions using AIM support the analytically obtained result as
well as the results in [7]. Finally, we compute the eigenfunctions and show,
pictorially, how the perturbed soap film evolves in time.
