  The illumination of an accretion disk around a black hole or neutron star by
the central compact object or the disk itself often determines its spectrum,
stability, and dynamics. The transport of radiation within the disk is in
general a multi-dimensional, non-axisymmetric problem, which is challenging to
solve. Here, I present a method of decomposing the radiative transfer equation
that describes absorption, emission, and Compton scattering in an obliquely
illuminated disk into a set of four one-dimensional transfer equations. I show
that the exact calculation of the ionization balance and radiation heating of
the accretion disk requires the solution of only one of the one-dimensional
equations, which can be solved using existing numerical methods. I present a
variant of the Feautrier method for solving the full set of equations, which
accounts for the fact that the scattering kernels in the individual transfer
equations are not forward-backward symmetric. I then apply this method in
calculating the albedo of a cold, geometrically thin accretion disk.
