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arXiv · 2503.09178

Spectral Method for 1-D Neutron Transport Equation

Haonan Zhang·Huiyuan Li·Zhimin Zhang
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Abstract

In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension with the Legendre-Gauss collocation scheme in the directional dimension. The directional integral in the original problem is discretized with Legendre-Gauss quadrature. We furnish a rigorous proof of the solvability of this scheme and, to our best knowledge, conduct a comprehensive error analysis for the first time. Notably, the order of convergence is optimal in the directional dimension, while in the spatial dimension, it is suboptimal and, importantly, non-improvable. Finally, we verify the computational efficiency and error characteristics of the scheme through several numerical examples.

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Haonan Zhang, Huiyuan Li, Zhimin Zhang. 2025-03-12. Spectral Method for 1-D Neutron Transport Equation. https://arxiv.org/abs/2503.09178

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