Short course on "Introduction to Geometric Numerical Integration for PDEs"
20.08 - 22.08, 1C-03 - Erwan Faou
Introduction to Geometric Numerical Integration for PDEs
In this lecture, I will mainly consider the numerical integration of the nonlinear Schrödinger equation over long times and discuss in particular the numerical stability of solitons in the one dimensional case. I will explain the phenomenon of time and space resonances, and show that under some restriction between the time and space discretization parameter, we can prove some orbital stability result for numerical schemes.