  The SP3 approximation of the neutron transport equation allows improving the
accuracy for both static and transient simulations for reactor core analysis
compared with the neutron diffusion theory. Besides, the SP3 calculation costs
are much less than higher order transport methods (SN or PN). Another advantage
of the SP3 approximation is a similar structure of equations that is used in
the diffusion method. Therefore, there is no difficulty to implement the SP3
solution option to the multi-group neutron diffusion codes. In this work, the
application of the SP3 methodology based on solution of the {\lambda}- and
{\alpha}-spectral problems has been tested for the IAEA-2D and HWR reactor
benchmark tests. The FEM is chosen to achieve the 3D geometrical generality,
using GMSH as a generic mesh generator. The results calculated with the
diffusion and SP3 methods are compared with the reference transport calculation
results. It was found for the HWR reactor test that some eigenvalues are
complex when calculating using both diffusion and SP3 options.
