2006
DOI: 10.1016/j.jcp.2006.04.019
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Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates

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Cited by 142 publications
(133 citation statements)
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“…In particular, we show that there is a great interest in considering the pseudo-spectral approximation rather than the finite difference scheme. A similar study has been conducted by Bao, Chern & Lim [21], for Ω = 0, where the authors show that BESP provides a spectral precision compared with BEFD.…”
Section: Besp or Befd? This Is Another Questionsupporting
confidence: 65%
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“…In particular, we show that there is a great interest in considering the pseudo-spectral approximation rather than the finite difference scheme. A similar study has been conducted by Bao, Chern & Lim [21], for Ω = 0, where the authors show that BESP provides a spectral precision compared with BEFD.…”
Section: Besp or Befd? This Is Another Questionsupporting
confidence: 65%
“…An alternative solution consists in considering a matrix-free iterative method. A first approach, introduced by Bao et al [21] for non rotating GPEs, is based on stationary (fixed-point) methods. It has been next extended to rotating BEC by Zeng & Zhang [124].…”
Section: Solving Besp Linear Systems: the Fixed Point Method Its Limmentioning
confidence: 99%
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“…ground state and excited states, is a major question in quantum physics, most particularly for BECs. Such a problem corresponds [9,10,11,16,17,18,19] to computing a real number µ and a space dependent function φ which satisfies the equation…”
Section: Introductionmentioning
confidence: 99%
“…To numerically determine (µ, φ), a well-known method is the so-called imaginary time method [9,10,11,16,17,18,19,20,23] which is also designated as a Continuous Normalized Gradient Flow (CNGF) method in the Applied Mathematics literature. It consists in solving (1) in imaginary-time, i.e.…”
Section: Introductionmentioning
confidence: 99%