Numerical solutions of diffusion equations in multi-dimensional slab geometry by Fourier expansions

Solutions of multi-dimensional neutron diffusion equations in Cartesian coordinates are obtained in the form of regionwise multi-dimensional Fourier series. Equations for two- and three-dimensional problems are derived. A critical and a source problem in two dimensions, and a one-regional source problem in three dimensions are numerically studied. Two kinds of Fourier series are numerically examined from the viewpoint of rapidity of convergence of the series. To obtain the value of the flux more accurately, a method is presented which contributes to improvement of the flux profile. (auth.)