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Titel
Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross-Pitaevskii equations
Autor*in
Harald Hofstätter
Technische Universität Wien
Autor*in
Othmar Koch
Technische Universität Wien
Autor*in
Othmar Koch
Technische Universität Wien
... show all
Abstract
A convergence analysis of time-splitting pseudo-spectral methods adapted for time-dependent Gross-Pitaevskii equations with additional rotation term is given. For the time integration high-order exponential operator splitting methods are studied, and the space discretization relies on the generalized-Laguerre-Fourier spectral method with respect to the (x,y)-variables as well as the Hermite spectral method in the z-direction. Essential ingredients in the stability and error analysis are a general functional analytic framework of abstract nonlinear evolution equations, fractional power spaces defined by the principal linear part, a Sobolev-type inequality in a curved rectangle, and results on the asymptotical distribution of the nodes and weights associated with Gauss-Laguerre quadrature. The obtained global error estimate ensures that the nonstiff convergence order of the time integrator and the spectral accuracy of the spatial discretization are retained, provided that the problem data satisfy suitable regularity requirements. A numerical example confirms the theoretical convergence estimate.
Stichwort
Time-dependent Gross-Pitaevskii equation with rotation termNonlinear Schrödinger equationFull discretizationGeneralized-Laguerre-Fourier-Hermite pseudo-spectral methodHigh-order time-splitting methodStabilityLocal errorConvergence
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:423907
Erschienen in
Titel
Numerische Mathematik
Band
127
Ausgabe
2
Seitenanfang
315
Seitenende
364
Verlag
Springer
Projektnummer
P24157-N13 – Austrian Science Fund (FWF)
Verfügbarkeitsdatum
2015-07-01
Datum der Annahme zur Veröffentlichung
2014-06
Zugänglichkeit

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