  We consider radially symmetric capillary surfaces that are described by
bounded generating curves. We use the arc-length representation of the
differential equations for these surfaces to allow for vertical points and
inflection points along the generating curve. These considerations admit
capillary tubes, sessile drops, and fluids in annular tubes as well as other
examples.
  We present a multi-scale pseudo-spectral method for approximating solutions
of the associated boundary value problems based on interpolation by Chebyshev
polynomials. The multi-scale approach is based on a domain decomposition with
adaptive refinements within each sub-domain.
