🚀 go-pugleaf

I need to solve a singular (2nd order) eigenvalue problem on [0, inf.) which, 
in general, has not only a regular singularity at the origin, but also at some 
interior location where the solution itself may also be unbounded.  The interior
singularity can be bypassed by integrating along an indented contour in the 
complex plane which can be chosen using (related) physical considerations.  
However, the endpoint singularity has led to in considerable difficulties
in the numerics which usually get attracted to a different eigenvalue than 
the one I would like to track or oscillate between some two eigenvalues as
I vary another controlling parameter in the problem.   

In order to get a handle on the global spectrum of this equation, one may
examine a simpler equation corresponding to a particular asymptotic limit, viz.,
           y'' - (1 - 1/x*x) y = 0;   y(0) = y(inf.) = 0,
which does not have any interior singularity.  It is also possible to express
the solutions to this equation in terms of modified Bessel function solutions 
of an imaginary order; but that does not help much. Unfortunately, even for 
this simpler equation, the numerics failed to exhibit convergence with respect 
to grid size and/or choice of the trucated domain. 
 
During a search for robust, canned public domain routines which also accomplish 
the same task, I came across the SLEIGN code by Bailey et. al. which has been 
modified recently and published as TOMS algorithm 700.  However, the netlib 
archives at ORNL do not seem to go beyond algorithms 686.  Does anyone have an 
idea as to whether this code can also be copied from some other site of 
archives?

Suggestions regarding other comparable codes, and their availability would
also be welcome.  I know about the D02KEF routine from the NAG library, but  
have no access to NAG.  In their 1968 article in TOMS, Bailley et. al. mention 
that singulat Sturm-Liouville cases are usually treated on a case by case basis,
although no references are given.  Therefore, related references would be
appreciated as well.

Thanks in advance to all.

- Meelan Choudhari

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