Chebyshev spectral-SN method for the neutron transport equation

We study convergence of a combined spectral and (SN) discrete ordinates approximation for a multidimensional, steady state, linear transport problem with isotropic scattering. The procedure is based on expansion of the angular flux in a truncated series of Chebyshev polynomials in spatial variables that results in the transformation of the multidimensional problems into a set of one-dimensional problems. The convergence of this approach is studied in the context of the discrete-ordinates equations based on a special quadrature rule for the scattering integral. The discrete-ordinates and quadrature errors are expanded in truncated series of Chebyshev polynomials of degree @? L, and the convergence is derived assuming L @? @s"t - 4@p@s"s, where @s"t and @s"s are total- and scattering cross-sections, respectively.

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