  The time-dependent numerical renormalization group method (TDNRG) [Anders et
al., Phys. Rev. Lett. {\bf 95}, 196801 (2005)] was recently generalized to
multiple quenches and arbitrary finite temperatures [Nghiem et al., Phys. Rev.
B {\bf 89}, 075118 (2014)] by using the full density matrix approach
[Weichselbaum et al., Phys. Rev. Lett. {\bf 99}, 076402 (2007)]. In this paper,
we numerically implement this formalism to study the response of a quantum
impurity system to a general pulse and periodic driving which are approximated
by a sufficient number of quenches. We show how the NRG approximation affects
the trace of the projected density matrices and the continuity of the
time-evolution of a local observable. For the general pulse case, the local
observable in the long-time limit exhibits a dependence on the switch-on time,
the time interval between the first and last quenches, as well as on the pulse
shape. In particular, the long-time limit is improved for longer switch-on
times and smoother pulses. This lends support to our earlier suggestion that
the long-time limit of observables can be improved by replacing a sudden large
quench by a sequence of smaller ones acting over a finite time-interval: longer
switch-on times and smoother pulses, i.e., increased adiabaticity, favor
relaxation of the system to its correct thermodynamic long-time limit. For the
case of periodic driving, we compare the TDNRG results to exact analytic ones
for the non-interacting resonant level model, finding better agreement at short
to intermediate time scales in the case of smoother driving. Finally, we
demonstrate the validity of the multiple-quench TDNRG formalism for arbitrary
temperatures by studying the time-evolution of the occupation number in the
Anderson impurity model in response to a periodic switching of the local level
from the mixed valence to the Kondo regime at finite temperatures.
