A two group analytical approximation solution for an external source problem without separation of space and time

This work presents the development of analytical approximation solutions for a space–time dependent neutron transport problem in two energy groups for a one dimensional system consisting of a homogenized medium with a localized external source. The approximation solutions are developed using Green’s functions, the influence of the delayed neutrons is not considered. Qualitative results for a given system are analyzed. A detailed comparison of the developed analytical approximation solutions with solutions with one energy group diffusion and P1 equation without separation of space and time is given.