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Most of the neutrons seen in the habitable environment of spacecraft in LEO are produced in local materials of the spacecraft structures by the impact of the LEO radiation environment. There are two components of the neutron spectra: one produced near the forward direction and a diffuse isotropic component. The forward component satisfies a Volterra equation and is solved by standard marching procedures. The diffuse component is generally of lower energy and nearly isotropically scattered as they diffuse through the spacecraft structures. Leakage at near boundaries marks the diffusion process and solutions are strongly dependent on forward and backward boundaries with minor contributions from lateral diffusion along spacecraft wall structures. The diffuse neutron equation is solved using multigroup methods with impressed forward and backward boundary conditions.