[{"type":"report","title":"Lowregularity exponential-type integrators for semilinear Schr\u00f6dinger equations","issued":{"date-parts":[["2017"]]},"DOI":"10.5445\/IR\/1000069444","author":[{"family":"Ostermann","given":"Alexander"},{"family":"Schratz","given":"Katharina"}],"publisher":"KIT","publisher-place":"Karlsruhe","ISSN":"2365-662X","collection-title":"CRC 1173","abstract":"We introduce low regularity exponential-type integrators for nonlinear Schr\u00f6dinger 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 Schr\u00f6dinger 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.","keyword":"nonlinear Schro\u0308dinger equations, exponential-type time integrator, low regularity, convergence","number-of-pages":24,"kit-publication-id":"1000069444"}]