  Solutions of Rough Differential Equations (RDE) may be defined as paths whose
increments are close to an approximation of the associated flow. They are
constructed through a discrete scheme using a non-linear sewing lemma. In this
article, we show that such solutions also solve a fixed point problem by
exhibiting a suitable functional. Convergence then follows from consistency and
stability, two notions that are adapted to our framework. In addition, we show
that uniqueness and convergence of discrete approximations is a generic
property, meaning that it holds excepted for a set of vector fields and
starting points which is of Baire first category. At last, we show that
Brownian flows are almost surely unique solutions to RDE associated to
Lipschitz flows. The later property yields almost sure convergence of Milstein
schemes.
