Calculation of the diffusion lengths for one-speed neutron in a slab using higher order first kind of the Chebyshev polynomials approximation

In this study, the neutron transport equation is solved for diffusion length problem in a homogeneous isotropic slab without source using first the conventional Legendre polynomials (PN) method and then the first kind of the Chebyshev polynomials method (TN). Firstly, the one-dimensional transport equation is solved using both methods and higher order moment equations are derived. Then, higher order linear differential equations with constant coefficients are obtained by putting these moment equations into each other. Finally, diffusion lengths are calculated for various scattering parameters by taking the inverse of the smallest root of the characteristic equations of the differential equations.