  We investigate the Coulomb breakup of $^{11}$Be halo nuclei on a heavy target
from intermediate (70 MeV/nucleon) to low energies (5 MeV/nucleon) within the
non-perturbative time-dependent approach. The convergence of the computational
scheme is demonstrated in this energy range including \textit{n}+$^{10}$Be
low-lying resonances in different partial and spin states. We have found a
considerable contribution of the $5/2^{+}$ resonance ($E_{r}$= 1.23 MeV) to the
breakup cross section at 30 MeV/nucleon and lower, while at higher energies,
the resonant states $3/2^{-}$ and $3/2^{+}$ (with $E_{r}$= 2.78 and 3.3 MeV)
make most visible contributions. The obtained results are in good agreement
with experimental data available at 69 and 72 MeV/nucleon. Comparison with the
existing theoretical calculations of other authors for 20 and 30 MeV/nucleon is
also made. The developed computational scheme opens new possibilities in the
investigation of the Coulomb, as well as nuclear, breakup of other halo nuclei
on heavy and light targets.
