Multigroup neutron transport theory in plane geometry

The multigroup form of the transport equation describing the steady state population of neutrons in a plane geometry is studied. The existing techniques of finding numerical solutions to the transport equation in the discrete ordinate approximation are considered in relation to the deep penetration problem of reactor shielding theory. Some of the computational difficulties are examined and a major one found to be the excessive time used in iterating the equation over a large number of mesh points.