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

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