  By instantaneously changing a global parameter in an extended quantum system,
an initially equilibrated state will afterwards undergo a complex
non-equilibrium unitary evolution whose description is extremely challenging. A
non-perturbative method giving a controlled error in the long time limit
remained highly desirable to understand general features of the quench induced
quantum dynamics. In this paper we show how integrability (via the algebraic
Bethe ansatz) gives one numerical access, in a nearly exact manner, to the
dynamics resulting from a global interaction quench of an ensemble of fermions
with pairing interactions (Richardson's model). This possibility is deeply
linked to the specific structure of this particular integrable model which
gives simple expressions for the scalar product of eigenstates of two different
Hamiltonians. We show how, despite the fact that a sudden quench can create
excitations at any frequency, a drastic truncation of the Hilbert space can be
carried out therefore allowing access to large systems. The small truncation
error which results does not change with time and consequently the method
grants access to a controlled description of the long time behavior which is a
hard to reach limit with other numerical approaches.
