Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation
Abstract:
We investigate the Lie and the Strang splitting for the cubic nonlinear Schrödinger equation on the full space and on the torus in up to three spatial dimensions. We prove that the Strang splitting converges in L2 with order 1 + for initial values in H2+2 with 2 (0; 1) and that the Lie splitting converges with order one for initial values in H2.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Institut für Angewandte und Numerische Mathematik (IANM) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2016 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X urn:nbn:de:swb:90-518883 KITopen-ID: 1000051888 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 20 S. |
| Serie | CRC 1173 ; 2016/3 |
| Schlagwörter | Nonlinear Schrödinger equation, Strang splitting, Lie splitting, error analysis, stability, fractional onvergence order, interpolation |