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In this work, a discrete ordinates solution for a neutron transport problem in one-dimensional Cartesian geometry is presented. In order to evaluate the efficiency of the half-range quadrature scheme, the Analytical Discrete Ordinates method (ADO) is used to solve two classes of problems in finite and homogeneous media (with isotropic and linear anisotropic scattering), for steady-state regime, without inner source and prescribed boundary conditions. Numerical results for the scalar fluxes were obtained and comparisons with other works in the literature were made. The versatility of the use of quadratures has always been seen as an advantage of the ADO method which, besides providing accurate results at a low computational cost, has a simpler approach, allowing the use of free software distribution for the simulations. In the results analysis, it was verified that the use of the half-range quadrature was able to accelerate the convergence, mainly in linearly anisotropic problems.

The influence of half-range quadrature scheme on ADO method convergence