Conference abstracts

Session B1 - Computational Dynamics

July 13, 15:30 ~ 16:00 - Room B1

Numerical algorithms and a-posteriori verification of periodic orbits of the Kuramoto-Sivashinsky equation.

Jordi-Lluís Figueras

Uppsala Univesrity, Sweden   -   figueras@math.uu.se

In this talk we will present a numerical algorithm for the computation of (hyperbolic) periodic orbits of the 1-D Kuramoto-Sivashinsky equation \[ u_t+\nu u_{xxxx}+u_{xx}+u u_x = 0, \] with $\nu>0$.

This numerical algorithm consists on applying a suitable quasi-Newton scheme. In order to do this, we need to rewrite the invariance equation that must satisfy a periodic orbit in a form that its linearization around an approximate solution is a bounded operator. We will also show how this methodology can be used to compute a-posteriori estimates of the errors of the solutions computed, leading to the rigorous verification of the existence of the periodic orbit.

If time permits, we will finish showing some numerical outputs of the algorithms presented along the talk.

Joint work with Rafael de la Llave..

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