  A Green's function based solver for the modified Bessel equation has been
developed with the primary motivation of solving the Poisson equation in
cylindrical geometries. The method is implemented using a Discrete Hankel
Transform and a Green's function based on the modified Bessel functions of the
first and second kind. The computation of these Bessel functions has been
implemented to avoid scaling problems due to their exponential and singular
behavior, allowing the method to be used for large order problems, as would
arise in solving the Poisson equation with a dense azimuthal grid. The method
has been tested on monotonically decaying and oscillatory inputs, checking for
errors due to interpolation and/or aliasing. The error has been found to reach
machine precision and to have computational time linearly proportional to the
number of nodes.
