One of the most important targets in nuclear safety analyses is the fast and accurate computation of the power evolution inside of the reactor core.The distribution of neutrons can be described by the neutron transport Boltzmann equation.The solution of this equation for realistic nuclear reactors is not straightforward, and therefore, numerical approximations must be considered.First, the thesis is focused on the attainment of the solution for several steadystate problems associated with neutron diffusion problem: the λ-modes, the γ-modes and the α-modes problems.A high order finite element method is used for the spatial discretization.Several characteristics of each type of spectral problem are compared and analyzed on different reactors.