On equiconvergence of ultraspherical polynomials solution of one-speed neutron transport equation

Ultraspherical-polynomials approximation to the radiative heat transfer in a slab with reflective boundaries

“…where δ is the Dirac's delta function, B is the linear anisotropy coefficient, α and β are forward and backward scattering probabilities in a collision, respectively [15]. Note that, for linearly anisotropic scattering, taking α = β = 0 and scaling by a factor of 2 in order to conform to the conventional form of the radiative transfer equation, Eq.…”

“…(13) into Eq. (9), and taking ultraspherical moment of both sides [15], the recurrence relation for three consecutive moments of the angular flux are obtained as…”

“…Compatibility of Eqs. (15) is assured if the determinant of coefficients vanishes, which is equivalent to using the well-known closure relationship [7],…”

“…In a recent study by Yilmazer and Tombakoglu [15], all ultraspherical-polynomials approximations have been incorporated into a single formulation to obtain eigenspectrum of the transport operator, which was then applied to slab-criticality problems of neutron transport.…”