Discrete ordinates (S-N) method for the first solution of the transport equation using Chebyshev polynomials

Abstract

First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied. The neutrons are assumed to be scattered isotropically through the medium. Then the discrete ordinates form of the transport equation is solved for the eigenvalue spectrum using the Chebyshev polynomials of second kind in the neutron angular flux. Therefore, the calculated eigenvalues for various values of the co, the mean number of secondary neutrons per collision, are given in the tables using the Gauss-Chebyshev quadrature set.