In this report the problem is considered of determining neutron flux distributions in reactors consisting of discrete regions of substantially different nuclear properties. Starting with these equations the problem is considered of determining the flux in one of the energy groups given the spatial flux distribution of the next higher energy group. The problem is handled by converting the differential equation with source term to an integral equation; under appropriate conditions the integral equation may be solved by a numerical iterative procedure. The conditions under which this may be done are discussed and formulas are developed for placing bounds on the errors. In addition the technique of obtaining flux distributions in complicated configurations by additive and multiplicative superposition of flux distributions of simpler configurations is considered. Expressions are derived for estimating the errors made in using these methods. A number of simple examples are presented.