  Stability of time domain integral equation (TDIE) solvers has remained an
elusive goal for many years. Advancement of this research has largely
progressed on four fronts: (1) Exact integration, (2) Lubich quadrature, (3)
smooth temporal basis functions, and (4) Space-time separation of convolutions
with the retarded potential. The latter method was explored in [Pray et al.
IEEE TAP 2012]. This method's efficacy in stabilizing solutions to the time
domain electric field integral equation (TD-EFIE) was demonstrated on first
order surface descriptions (flat elements) in tandem with 0th order functions
as the temporal basis. In this work, we develop the methodology necessary to
extend to higher order surface descriptions as well as to enable its use with
higher order temporal basis functions. These higher order temporal basis
functions are used in a Galerkin framework. A number of results that
demonstrate convergence, stability, and applicability are presented.
