  The one-dimensional Fermi-Hubbard model is used as testbed for strong global
parameter quenches. With the aid of iterated equations of motion in combination
with a suitable scalar product for operators we describe the dynamics and the
long-term behavior in particular of the system after interaction quenches. This
becomes possible because the employed approximation allows for oscillatory
dynamics avoiding spurious divergences. The infinite-time behavior is captured
by an analytical approach based on stationary phases; no numerical averages
over long times need to be computed. We study the most relevant frequencies in
the dynamics after the quench and find that the local interaction $U$ as well
as the band width $W$ dominate. In contrast to former studies a crossover
instead of a sharp dynamical transition depending on the strength of the quench
is identified. For weak quenches the band width is more important while for
strong quenches the local interaction $U$ dominates.
