Exponential Supplementary Equations for S_N Methods: The One-Dimensional Case

The use of supplementary exponential equations to solve the transport equation by means of the discrete ordinate method has been studied. It is shown that the set of final equations so obtained can be easily and quickly solved on the computer using the same iterative procedure employed in standard S_N codes. The new method is implemented on ANISN and DOT-III codes. This work refers only to the one-dimensional case. Extensive numerical experiments for neutrons and gamma rays showed that the exponential scheme increases the convergence rate of the iterative procedure and always overestimates the “reference solution” by very small amounts for the finest mesh size and by reasonable amounts for the largest mesh size. For its own structure, the exponential method always gives positive angular fluxes without any adjustment techniques provided the source is non-negative.