R. S. Varga and M. A. Martino, The theory for the numerical solution of time-dependent and time-independent multigroup diffusion equations, Proc. of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy 16, pp. 570-577, Pergamon Press, London, 1959.
It has long been recognized that the multigroup diffusion theory approximations to the transport equation give very useful information in the nuclear design of many types of reactors. In recent years, the solutions of these multigroup diffusion equations have been attacked numerically by means of large-scale digital computers. In this paper, mathematically rigorous foundations are given for the time-dependent and time-independent multigroup approximations, not only for the discrete (space) numerical problem consisting of a finite numer of mesh (lattice) points, but for the continuous space problem as well. In so doing, the discrete numerical approximations to the multigroup diffusion equations, as solved on digital machines, will be shown to be well-set.