  We consider in this contribution a simplified idealized one-dimensional
coupled model for neutronics and thermo-hydraulics under the low Mach number
approximation. We propose a numerical method treating globally the coupled
problem for finding its unique solution. Simultaneously, we use incomplete
elliptic integrals to represent analytically the neutron flux. Both methods
match perfectly. Note that the multiplication factor, classical output of
neutronics problems, depends considerably of the representation of the cross
sections.
