A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries

Ming-Chih Lai*, Chung Yin Huang, Te-Sheng Lin

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    12 Scopus citations

    Abstract

    We develop a simple Dufort-Frankel-type scheme for solving the time-dependent Gross-Pitaevskii equation (GPE). The GPE is a nonlinear Schrodinger equation describing the Bose-Einstein condensation (BEC) at very low temperature. Three different geometries including 1D spherically symmetric, 2D cylindrically symmetric, and 3D anisotropic Cartesian domains are considered. The present finite difference method is explicit, linearly unconditional stable and is able to handle the coordinate singularities in a natural way. Furthermore, the scheme is time reversible and satisfies a discrete analogue of density conservation law.

    Original languageEnglish
    Pages (from-to)624-638
    Number of pages15
    JournalNumerical Methods for Partial Differential Equations
    Volume20
    Issue number4
    DOIs
    StatePublished - 1 Jul 2004

    Keywords

    • Bose-Einstein condensates
    • Dufort-Frankel scheme
    • Gross-Pitaevskii equation
    • Nonlinear Schrödinger equation

    Fingerprint

    Dive into the research topics of 'A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries'. Together they form a unique fingerprint.

    Cite this