The spectral nodal method applied to multigroup SN neutron transport problems in One-Dimensional geometry with Fixed-Source

The nodal methods, as deterministic models, form a class of numerical methods developed to generate accurate numerical solutions of the Boltzmann equation for neutron transport. These methods are algebraically and computationally more laborious than the traditional deterministic fine-mesh methods like the Diamond Difference method (DD). However, their numerical solution for traditional coarse-mesh problems is more accurate. For this reason, the nodal methods and their algorithms for direct and iterative solution schemes have been the subject of extensive research. In this paper we propose a simpler methodology for the development of a method of spectral nodal class which is tested as an initial study of the solutions (spectral analysis) of the neutron transport equation in the formulation of discrete ordinates (SN), in one-dimensional geometry, multigroup energy approximation, isotropic scattering and considering homogeneous and heterogeneous domains. These results are compared with the traditional fine-mesh DD method and the spectral nodal methods, spectral Green's function (SGF) and Response Matrix (RM) to test their numerical accuracy, stability and consistency.