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Axford, Roy A. Grove, Travis Justin 2015-09-28T14:51:01Z 2015-09-28T14:51:01Z 10000-01-01 2005 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. Made available in DSpace on 2015-09-28T14:51:01Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3199006.pdf: 11883280 bytes, checksum: 4653bf9c5959c07dbf2f6d6c3f6f6aef (MD5) Previous issue date: 2005 Embargo set by: Seth Robbins for item 87184 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 527 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2005. http://hdl.handle.net/2142/85903 (MiAaPQ)AAI3199006 eng Engineering, Nuclear Application of Lie Groups to Discretizing Nuclear Engineering Problems text Nuclear Engineering Nuclear Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.