One speed black sphere problem: Some benchmark results

Benchmark numerical results for the black sphere problem (one speed, isotropic scattering) are reported by extending some previous computations on the relevant integral transport equation [Loyalka, S.K., 1975. A numerical method for solving integral equations of neutron transport. Nuclear Science and Engineering 56, 317-319]. Spheres of radii (non-dimensionalized in terms of a mean free path) in the range 10−6-106 are considered, and a transformation of the range from (R, ∞) to (0, 1), is used together with successively high order quadratures, and high precision in all computations. Two different quadrature sets (Gauss-Legendre and Gauss-Kronrod) are explored and convergent and accurate numerical results for the extrapolation distance as well as the density profile are obtained.