  In this paper we report on the results of a numerical study of the nonlinear
time-dependent Bardeen--Cooper--Schrieffer (BCS) equations, often also denoted
as Bogoliubov--de--Gennes (BdG) equations, for a one-dimensional system of
fermions with contact interaction. We show that, even above the critical
temperature, the full equations and their linear approximation give rise to
completely different evolutions. In contrast to its linearization, the full
nonlinear equation does not show any diffusive behavior in the order parameter.
This means that the order parameter does not follow a Ginzburg--Landau-type of
equation, in accordance with a recent theoretical results. We include a full
description on the numerical implementation of the partial differential BCS\
BdG equations.
