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<p>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.</p>

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Spectral Method for 1-D Neutron Transport Equation

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • Haonan Zhang,
  • Huiyuan Li,
  • Zhimin Zhang

摘要

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.