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

Comparing the full time-dependent Bogoliubov--de-Gennes equations to their linear approximation: A numerical investigation