numerical caseology by Lagrange interpolation for the 1D neutron transport equation in a slab

TL;DR

This paper introduces a new numerical method called Lagrange order N method (LNM) for solving the 1D neutron transport equation, combining high precision with simplicity using Lagrangian polynomials based on Case's singular eigenfunction expansion.

Contribution

The paper presents the LNM, a novel numerical approach that improves accuracy and simplicity in solving the 1D neutron transport equation using Lagrangian basis functions.

Findings

LNM achieves high precision in numerical solutions.

LNM offers a more convenient basis compared to existing methods.

The method simplifies the implementation of analytical solutions.

Abstract

Here, we are concerned with a new, highly precise, numerical solution to the 1D neutron transport equation based on Cases analytical singular eigenfunction expansion (SEE). While a considerable number numerical solutions currently exist, understandably, because of its complexity, even in 1D, there are only a few truly analytical solutions to the neutron transport equation. In 1960, Case introduced a consistent theory of the SEE for a variety of idealized transport problems and forever changed the landscape of analytical transport theory. Several numerical methods including the FN method were based on the theory. What is presented is yet another, called the Lagrange order N method (LNM), featuring the simplicity and precision of the FN method, but for a more convenient and natural Lagrangian polynomial basis.