Milne problem for non-absorbing medium with extremely anisotropic scattering kernel in the case of specular and diffuse reflecting boundaries

The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic scattering kernel which combines forward and backward scatterings (extremely anisotropic scattering) for a non-absorbing medium with specular and diffuse reflection boundary conditions. In order to calculate the extrapolated endpoint for the Milne problem, Legendre polynomial approximation (\(P_{N}\) method) is applied and numerical results are tabulated for selected cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with the existing results in literature.