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 central 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 and with results gained by the time dependent diffusion equation without separation of space and time is given.