  We completed the development of simulation code that is designed to study the
behavior of a conjectured dark matter galactic halo that is in the form of a
Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii
equation, which can be solved numerically using the Crank-Nicholson method. The
gravitational potential, in turn, is described by Poisson's equation, that can
be solved using the relaxation method. Our code combines these two methods to
study the time evolution of a self-gravitating BEC. The inefficiency of the
relaxation method is balanced by the fact that in subsequent time iterations,
previously computed values of the gravitational field serve as very good
initial estimates. The code is robust (as evidenced by its stability on coarse
grids) and efficient enough to simulate the evolution of a system over the
course of 1E9 years using a finer (100x100x100) spatial grid, in less than a
day of processor time on a contemporary desktop computer.
