A Numerical-Analytical Solution of the One-Dimensional and Monoenergetic Neutron Transport Equation for Eigenvalue Problems

Alexandre G. de O. Cordeiro; Adilson Costa da Silva; Sergio de Oliveira Vellozo

doi:10.15392/2319-0612.2026.3018

Authors

Alexandre G. de O. Cordeiro Military Institute of Engineering
Adilson Costa da Silva Federal University of Rio de Janeiro
Sérgio de Oliveira Vellozo Military Institute of Engineering

DOI:

https://doi.org/10.15392/2319-0612.2026.3018

Keywords:

Neutron Transport Equation, Numerical-Analytical Solutions, Numerical Methods, Criticality Calculations

Abstract

The study of neutron behavior and interactions within the core of a nuclear reactor is essential for ensuring criticality control. The most accurate deterministic framework for modeling these phenomena is the Neutron Transport Equation, which, with the exception of stochastic methods such as Monte Carlo, is typically solved using fine-mesh numerical methods. However, such approaches often entail considerable computational costs to achieve high-fidelity results. In this work, we propose a numerical-analytical solution to the one-dimensional, monoenergetic neutron transport equation with isotropic scattering, formulated for eigenvalue problems and employing the discrete ordinates (SN) method. The proposed formulation is presented through a fully explicit and self-contained step-by-step derivation, emphasizing transparency and reproducibility of the numerical-analytical approach. To assess the accuracy and efficiency of the proposed approach, results were compared with those obtained from a purely numerical method developed in this study, as well as with benchmark solutions reported in the literature. In all cases, the proposed method exhibited excellent agreement with reference data, along with a significant reduction in computational time.

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