Application of Lie Groups to Discretizing Nuclear Engineering Problems

527 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005.In addition, a method using groups of point transformations along with Noether's theorem is shown to generate a conservation law that can be used to create a two-term recurrence relation which calculates numerically exact Green's functions in one dimension for the time-independent neutron diffusion equation for Cartesian, cylindrical, and spherical geometries. This method will be expanded to constructing two-term recurrence relations for an arbitrary number of spatial regions, as well as detailing starting point values for type 2 and type 3 homogeneous endpoint boundary conditions. Finally, the method of constructing two-term recurrence relations will be applied to Green's function matrices for the one-dimensional time-independent neutron diffusion equation for Cartesian, cylindrical, and spherical geometries. In particular, two-term recurrence relations for the off-diagonal elements of the Green's function matrices will be derived, and the method is adapted to take into account discontinuities in the value of a function.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD