This thesis examines the UTD diffraction coefficient's limitations in accuracy for a half plane and a wedge at low frequency. The UTD solutions are developed for scattering by a strip and a square cylinder with diffraction considered as a local phenomenon. Single and multiple diffractions are considered, and both TE and TM polarizations are done.  As a benchmark, moment method solutions are developed for the strip and square cylinder. Pulse basis point matching is used after investigating its adequacy: some moment method codes that are available in the open literature were examined; in one instance some modifications were required to obtain satisfactory results. For the infinite edge, comparison is done with modal solutions and Sommerfeld's exact solution. The UTD diffraction solution reduces to Sommerfeld's exact solution when the edge is a half plane and the incident field is a plane wave. The equivalence of these cases is not obvious and is derived as part of this work. Other comparisons are made with results that are available in the literature.  It was found that UTD, when multiple diffraction is taken into account, can be used to compute scattered fields and surface currents for scatterers as small as 0.1 n in dimension, with a very high degree of accuracy. This is quite surprising, as UTD is generally expected to only work well with electrically large structures on the order of 1 n in size or larger