Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate

Shu-Ming Chang, Wen-Wei Lin*, Shih Feng Shieh

*Corresponding author for this work

Research output: Contribution to journalArticle

36 Scopus citations


In this paper, we propose two iterative methods, a Jacobi-type iteration (JI) and a Gauss-Seidel-type iteration (GSI), for the computation of energy states of the time-independent vector Gross-Pitaevskii equation (VGPE) which describes a multi-component Bose-Einstein condensate (BEC). A discretization of the VGPE leads to a nonlinear algebraic eigen-value problem (NAEP). We prove that the GSI method converges locally and linearly to a solution of the NAEP if and only if the associated minimized energy functional problem has a strictly local minimum. The GSI method can thus be used to compute ground states and positive bound states, as well as the corresponding energies of a multi-component BEC. Numerical experience shows that the GSI converges much faster than JI and converges globally within 10-20 steps.

Original languageEnglish
Pages (from-to)367-390
Number of pages24
JournalJournal of Computational Physics
Issue number1
StatePublished - 1 Jan 2005


  • Gauss-Seidel-type iteration
  • Gross-Pitaevskii equation
  • Multi-component Bose-Einstein condensate
  • Nonlinear eigenvalue problem

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