@Article{Ostermann2017,
author="Ostermann, Alexander
and Schratz, Katharina",
title="Low Regularity Exponential-Type Integrators for Semilinear Schr{\"o}dinger Equations",
journal="Foundations of Computational Mathematics",
year="2017",
month="May",
day="26",
abstract="We introduce low regularity exponential-type integrators for nonlinear Schr{\"o}dinger equations for which first-order convergence only requires the boundedness of one additional derivative of the solution. More precisely, we will prove first-order convergence in {\$}{\$}H^r{\$}{\$} H r for solutions in {\$}{\$}H^{\{}r+1{\}}{\$}{\$} H r + 1 (with {\$}{\$}r > d/2{\$}{\$} r > d / 2 ) of the derived schemes. This allows us lower regularity assumptions on the data than for instance required for classical splitting or exponential integration schemes. For one-dimensional quadratic Schr{\"o}dinger equations, we can even prove first-order convergence without any loss of regularity. Numerical experiments underline the favorable error behavior of the newly introduced exponential-type integrators for low regularity solutions compared to classical splitting and exponential integration schemes.",
issn="1615-3383",
doi="10.1007/s10208-017-9352-1",
url="https://doi.org/10.1007/s10208-017-9352-1"
}