On Choice of Trial Functions in Integro-Differential Variational Principles of Transport Theory

In several problems of particle transport, quantities of macroscopic interest can be related to stationary values of variational functionals based on general integro-differential equations and boundary conditions. Within the context of the jump (Milne’s) problem, it is shown how highly accurate results can be obtained by using trial functions based on the eigenfunctions of the relevant integro-differential equations. Such choices of trial functions should apply equally effectively to problems in curved geometries, both internal and external.