  The contrast current density volume integral equation, discretized with
piecewise constant spatial basis and test functions and Dirac-delta temporal
test functions and the piecewise polynomial temporal basis functions, results
in a causal implicit marching-on-in-time scheme that we refer to as the
marching-on-in-time contrast current density volume integral equation
(MOT-JVIE). The companion matrix stability analysis of the MOT-JVIE solver
shows that for a fixed spatial and temporal step size, the stability is
independent of the scatterer's dielectric contrast for quadratic spline
temporal basis functions. Whereas, Lagrange and cubic spline exhibit
instabilities at higher contrast. We relate this stability performance to the
expansion and testing procedure in time. We further illustrate the capabilities
of the MOT-JVIE based on quadratic spline temporal basis functions by:
comparing the MOT-JVIE solution to time-domain results from literature and
frequency-domain results from a commercial combined field integral equation
solver. Finally, we present a long time sequence for a high-constrast scatterer
discretized with 24,000 spatial unknowns.
