# Lowregularity exponential-type integrators for semilinear Schrödinger equations

Ostermann, Alexander; Schratz, Katharina

Abstract:
We introduce low regularity exponential-type integrators for nonlinear Schrödinger 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$^r$ for solutions in H$^r$$^+$$^1$ (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 Schrödinger 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.

 Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2017 Sprache Englisch Identifikator ISSN: 2365-662X URN: urn:nbn:de:swb:90-694449 KITopen-ID: 1000069444 Verlag KIT, Karlsruhe Umfang 24 S. Serie CRC 1173 ; 2017/11 Schlagworte nonlinear Schrödinger equations, exponential-type time integrator, low regularity, convergence
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft KITopen Landing Page