We discuss the numerical treatment of a nonlinear second order
boundary value problem in ordinary differential equations posed on
an unbounded domain which represents the density profile equation
for the description of the formation of microscopical bubbles in a
non-homogeneous fluid. For an efficient numerical solution the
problem is transformed to a finite interval and polynomial
collocation is applied to the resulting boundary value problem
with essential singularity. We demonstrate that this problem is
well-posed and the involved collocation methods show their
classical convergence order. Moreover, we investigate what problem
statement yields favorable conditioning of the associated
collocation equations. Thus, collocation methods provide a sound
basis for the implementation of a standard code equipped with an a
posteriori error estimate and an adaptive mesh selection
procedure. We present a code based on these algorithmic components
that we are currently developing especially for the numerical
solution of singular boundary value problems of arbitrary, mixed
order, which also admits to solve problems in an implicit
formulation. Finally, we compare our approach to a solution method
proposed in the literature and conclude that collocation is an
easy to use, reliable and highly accurate way to solve
problems of the present type.