Spectral analysis of the two-groups discrete ordinates method with isotropic scattering in three-dimensional cartesian geometry

In this work we perform a spectral analysis of the a nodal method to generate an new analytical solution for three-dimensional discrete ordinates problems with two energy groups and isotropic scattering in cartesian geometry. The present nodal method is based on the the spectral nodal methods for discrete ordinates problems, wherein the only approximation involved is the approximation for the transverse leakage terms. The S_N equations are integrated transversally and the solution is derived by seeking first the new general solution for the homogeneous part and then adding a particular solution. We choose a level symmetric quadrature set and we obtain the characteristic equation for the determination of the eigenvalues with multiplicity greater than or equal to unity. (author)