  The analytical solution of neutron transport equation has fascinated
mathematicians and physicists alike since the Milne half-space problem was
introduce in 1921 [1]. Numerous numerical solutions exist, but understandably,
there are only a few analytical solutions, with the prominent one being the
singular eigenfunction expansion (SEE) introduced by Case [2] in 1960. For the
half-space, the method, though yielding, an elegant analytical form resulting
from half-range completeness, requires numerical evaluation of complicated
integrals. In addition, one finds closed form analytical expressions only for
the infinite medium and half-space cases. One can find the flux in a slab only
iteratively. That is to say, in general one must expend a considerable
numerical effort to get highly precise benchmarks from SEE. As a result,
investigators have devised alternative methods, such as the CN [3], FN [4] and
Greens Function Method (GFM) [5] based on the SEE have been devised. These
methods take the SEE at their core and construct a numerical method around the
analytical form. The FN method in particular has been most successful in
generating highly precise benchmarks. No method yielding a precise numerical
solution has yet been based solely on a fundamental discretization until now.
Here, we show for the albedo problem with a source on the vacuum boundary of a
homogeneous medium, a precise numerical solution is possible via Lagrange
interpolation over a discrete set of directions.
