An analytic and symbolic analysis of a coupled thermo-neutronic problem

In this paper, we seek analytical approximate solutions of a problem coupling the neutronics equation and the thermal equation (using incomplete Elliptic integrals), and we compare these analytical approximate solutions to a numerical method for the coupled problem, using a Crank-Nicolson scheme for the thermal equation and an generalized eigenvalue problem for the neutronics equation. Both the approximate analytical methods and the numerical method amount to finding the multiplication factor
$k_{eff}$
(
$k_{eff}^{-1}$
is the generalized eigenvalue) as the unique solution of an equation. All methods yield values of
$k_{eff}$
close to each other with a difference of magnitude 10
⁻⁷
, which is much better than what is generally needed in neutronics.