A Numerical Study of the Method of Weighted Residuals

The variational method and region-balance method, both special cases of the more general method of weighted residuals, are each used as the formalism to develop a spatial expansion of the diffusion equation for two problems. These are 1)a spatially dependent spectrum problem for the purpose of computing the self-shielding in the ₂₄0Pu resonance and 2) a simple one-dimensional eigenvalue problem. In both instances numerical results indicate that the variational method is more accurate than the region-balance method. Of particular interest is the variational spatial-expansion approach to the eigenvalue problem. This may be a useful method for deriving a set of difference equations for the multigroup diffusion equation in that it should lead to an accurate representation of the flux with a relatively small number of mesh points.