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

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.