Low regularity error estimates for high dimensional nonlinear Schrödinger equations

Lun Ji; Alexander Ostermann

doi:10.1007/978-3-031-76988-7_13

paper

Low regularity error estimates for high dimensional nonlinear Schrödinger equations

arXiv:2312.11071 · doi:10.1007/978-3-031-76988-7_13

Abstract

The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schrödinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete Bourgain spaces in one and two space dimensions for initial data in $H^{s}$ with $0 < s \leq 2$ . Here, this analysis is extended to dimensions $d = 3, 4, 5$ for data satisfying $d /2 - 1 < s \leq 2$ . In this setting, convergence of order $s /2$ in $L^{2}$ is proven. Numerical examples illustrate these convergence results.