Contributed Talk
Low-regularity integration of NLS
University of Innsbruck, Austria
Abstract
Standard numerical integrators such as splitting methods or exponential integrators suffer from order reduction when applied to semi-linear dispersive problems with non-smooth initial data. In this talk, we focus on the cubic nonlinear Schrödinger equation with periodic boundary conditions. For such problems, we present and analyze (filtered) Fourier integrators that exhibit superior convergence rates at low regularity. Numerical examples illustrating the analytic results will be given.
This is joint work with Frédéric Rousset (Paris-Sud), Katharina Schratz (Sorbonne, Paris), Yifei Wu (Tianjin University, China) and Fangyan Yao (South China University, Guangzhou)