ANALYTICAL NUMERICAL-METHODS APPLIED TO LINEAR DISCONTINUOUS ANGULAR APPROXIMATIONS OF THE TRANSPORT-EQUATION IN SLAB GEOMETRY

In this paper we describe two analytical numerical methods applied to one-speed slab-geometry deep penetration transport problems. The linea r discontinuous (LD(N)) equations are used to approximate the monoener getic Boltzmann equation in slab geometry; they are obtained by consid ering a linear expansion of the angular flux inside each of the N elem ents of a uniform angular grid. The two analytical numerical methods a re referred to as the spectral Green's function (SGF) nodal method and the Laplace transform (LTLD(N)) method. The SGF nodal method and the LTLD(N) method generate numerical solutions to the LD(N) equations tha t are completely free of spatial approximations, apart from finite ari thmetic considerations. Numerical results to typical model problems an d suggestions for future work are also presented.