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Strang splitting for a semilinear Schrödinger equation with damping and forcing

Jahnke, Tobias; Mikl, Marcel; Schnaubelt, Roland

Abstract:
We propose and analyze a Strang splitting method for a cubic semilinear Schrödinger equation with forcing and damping terms. The nonlinear part is solved analytically, whereas the linear part - space derivatives, damping and forcing - is approximated by the exponential trapezoidal rule. The necessary operator exponentials and Ø-functions can be computed effciently by fast Fourier transforms if space is discretized by spectral collocation. We show wellposedness of the problem and H4(T) regularity of the solution for initial data in H4(T) and suficiently smooth forcing. Under these regularity assumptions, we prove a first-order error bound in H1(T) and a second-order error bound in L2(T) on bounded time-intervals. Nonlinear Schrödinger equation; Strang splitting; error analysis; stability; wellposedness; regularity.


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/1000052585
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-525852
KITopen ID: 1000052585
Verlag KIT, Karlsruhe
Umfang 26 S.
Serie CRC 1173 ; 2016/4
Schlagworte nonlinear Schrödinger equation, strang splitting, error analysis, stability, wellposedness, regularity
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