Numerical Integration of the Transport Equation with No Angular Truncation

For any given azimuth-independent scattering law, it is shown that the neutron transport equation with external source is rigorously equivalent to a coupled system of Fredholm integral equations. These are derived both for vacuum and periodic boundary conditions. A numerical integration scheme is given for solving these integral equations with no angular truncation error, thereby permitting the solution of the Boltzmann equation numerically, with no error but that in the spatial integration. All cross sections are permitted to be arbitrarily given functions of position, if desired.