  We describe a formalism for solving the BFKL equation with a coupling that
runs for momenta above a certain infrared cutoff. By suitably choosing matching
conditions proper account is taken of the fact that the BFKL diffusion implies
that the solution in the infrared (fixed coupling) regime depends upon the
solution in the ultraviolet (running coupling) regime and vice versa. Expanding
the BFKL kernel to a given order in the ratio of the transverse momenta allows
arbitrary accuracy to be achieved.
