A Spectral Representation of the Linear Multigroup Transport Problem

Abstract

In 1981, Kanal and Davies made the transformation of the fundamental equation of the one‐velocity linear transport theory by expanding the scattering function for the problem to be solved as a spectral integral over the complete set Case's eigenfunctions for a previously solved transport problem. The obtained equation represented a singular integral equation containing a spectral integral over the spectrum of the solved problem, whose kernel depends on the difference between the scattering function of the problem to be solved and that of the solved problem. As a matter of fact, the above authors derived mathematical reformulation of the well‐known Case's approach to the solution of the one‐dimensional equation of transport. Moreover, the above authors considered also several examples illustrating the validity of such reformulation. In this paper we generalize these results to the problems of the one‐dimensional linear multigroup transport theory.

Keywords:

• One‐velocity linear transport theory
• Multigroup transport problem
• Phase matrix function
• Spectral density