• Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross-Pitaevskii equations

  • 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.

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  • http://phaidra.univie.ac.at/o:423907

  • Wissenschaftlicher Artikel

  • Angenommene Version

  • Numerische Mathematik

  • 06.2014

  • 127

  • 2

  • 315-364

  • Springer

  • Englisch

  • Frei zugänglich

  • 01.07.2015

  • P24157-N13 – Fonds zur Förderung der wissenschaftlichen Forschung (FWF)

  • 0029-599X

  • Time-dependent Gross-Pitaevskii equation with rotation term; Nonlinear Schrödinger equation; Full discretization; Generalized-Laguerre-Fourier-Hermite pseudo-spectral method; High-order time-splitting method; Stability; Local error; Convergence

  • Dewey Dezimal Klassifikation → Naturwissenschaften und Mathematik → Mathematik → Numerical analysis