A variational treatment for the time dependent Boltzmann equation as a basis for numerical solutions conserving neutrons

A maximum principle for the time-dependent first-order Boltzmann equation is established in two independent ways:- by a generalized least squares method and by a method based on the properties of an appropriate bi-linear form. The second derivation suggests a metric for a Hilbert space which provides a geometrical interpretation of the variational principle. This interpretation leads to a Petrov-Galerkin method of Martin for time dependent transport. The maximum principle is used to define a figure of merit for the global error of any numerical solution for time dependent transport. The principle is used also to demonstrate the neutron conservation property of optimized numerical solutions, and the convergence of finite element methods based on the variational principle. (Author)