In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete- ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the S{sub}N equations. This procedure leads to a set of one-dimensional S{sub}N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub}N method, which consists in the application of the Laplace transform to the set of nodal SN equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub}N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub}N equations for N up to 16 and we begin the convergence of the S{sub}N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation.
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