The Variational Method for Problems of Neutron Diffusion and of Radiative Transfer

Abstract

The functional as proposed by R. E. Marshak for solving certain inhomogeneous integral equations by the variational method is modified in such a way that the simultaneous equations which determine the parameters become linear. Thus we can solve this type of integral equations with an accuracy as high as required without much labor. As an illustration we obtain by the present method an approximate solution of Milne's integral equation for the neutron density (or for the source function in the problem of radiative transfer) in a simple form. Our approximate solution agrees (for the first four figures) everywhere with the one computed by C. Mark from the exact solution.