A simple Dufort-Frankel-type scheme for the Gross-Pitaevskii equation of Bose-Einstein condensates on different geometries
✍ Scribed by Ming-Chih Lai; Chung-Yin Huang; Te-Sheng Lin
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 130 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0749-159X
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✦ Synopsis
Abstract
We develop a simple Dufort‐Frankel‐type scheme for solving the time‐dependent Gross‐Pitaevskii equation (GPE). The GPE is a nonlinear Schrödinger 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. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004