Newton Basin
Chanteperdrix Guilhem(mfn04)



To conclude this project, I have to explain why it is of great interest for a CFD engineer. But first let's come back on the use of Newton's Method to solve non-linear systems. More precisely :

Newton's Method for non-linear systems

I found a link with our  formation in [3] and [4], where R. Choquet consider the implicit numerical resolution of the compressible Navier-Stokes equations with the Newton's Method. We can resume what he introduced by :

The Navier-Stokes equations connection !

We all know that this choice is not used in industrial CFD codes, but it is interesting to see that it can be a way of solving the Navier-Stokes system, even if Newton's Method can lead to fractal !...

For future session, I think that it could be interesting to study the Newton's method applied to the polynomial x->x^3+ax-1, where a is a real parameter. I know that it exists some a for which there is bifurcations, see [5] for more details.

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