  A novel method for solving the linear radiative transport equation (RTE) in a
three-dimensional homogeneous medium is proposed and illustrated with numerical
examples. The method can be used with an arbitrary phase function A(s,s') with
the constraint that it depends only on the angle between the angular variables
s and s'. This corresponds to spherically symmetric (on average) random medium
constituents. Boundary conditions are considered in the slab and half-space
geometries. The approach developed in this paper is spectral. It allows for the
expansion of the solution to the RTE in terms of analytical functions of
angular and spatial variables to relatively high orders. The coefficients of
this expansion must be computed numerically. However, the computational
complexity of this task is much smaller than in the standard method of
spherical harmonics. The solutions obtained are especially convenient for
solving inverse problems associated with radiative transfer.
