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Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation

Eilinghoff, Johannes; Schnaubelt, Roland; Schratz, Katharina

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
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000051888
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-518883
KITopen ID: 1000051888
Verlag KIT, Karlsruhe
Umfang 20 S.
Serie CRC 1173 ; 2016/3
Schlagworte Nonlinear Schrödinger equation, Strang splitting, Lie splitting, error analysis, stability, fractional onvergence order, interpolation
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