Tschebyscheff Polynomial Approximation Method of the Neutron-Transport Equation

Abstract

The Tschebyscheff polynomial approximation method of the neutron-transport equation is developed. The relations between the relaxation constants in this approximation and the positive roots of TN+1(μ)=0 are derived. Using these relations, the necessary condition for reactor criticality is discussed. Application to Milne's problem leads to an explicit expression for extrapolated end point which is formally the same in the spherical-harmonics method. Numerical comparison of this method with the spherical-harmonics method verifies Conkie's conclusion [W. R. Conkie, Nuclear Sci. and Eng. 6, 260 (1959)] that, for weak absorbers, the spherical-harmonics method gives the values for extrapolated end point which is closer to the exact value than the TN method does while, for strong absorbers, the TN method gives closer value than the PL method does.