A nodal collocation method for the calculation of the lambda modes of the PL equations

PL equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the PL approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem.