Matthieu Brachet

In this talk, I will introduce numerical analysis notions such as convergence and stability for the advection equation (transport equation).

I will present operator for the approximation of derivative : the hermitian fourth order derivative, and two methods for the time discretisation : a Runge-Kutta method and the exponential integrator.

We will study this two schemes and analyse their properties of stability, convergence, conservation.

Even if an analytial solution is available, it will give us a good idea of some numerical questions.

If we have enough time, I will introduce the extension of this works on the sphere.