On a discretised spectral approximation in neutron transport theory

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Abstract
An approximation method significantly different from existing ones is developed for the one-speed neutron transport equation. The theory is based on the singular eigenfunction method, and is founded on the new concepts of (i) a rational function approximation of the Case singular eigenfunction and (ii) discretisation of the continuous spectrum (0,1) of the half-range transport problem using the roots of a set of polynomials orthogonal in (0,1) with respect to a simple closed-form accurate approximation of the half-range weight function W ( mu ). A sample numerical example is given to illustrate the application of the theory.