A spectral collocation method for a rotating BoseEinstein condensation in optical lattices
We extend the study of spectral collocation methods (SCM) in Li et al. (2009) [1] for semilinear elliptic eigenvalue problems to that for a rotating BoseEinstein condensation (BEC) and a rotating BEC in optical lattices. We apply the Lagrange interpolants using the LegendreGaussLobatto points to derive error bounds for the SCM. The optimal error bounds are derived for both H1 H 1 -norm and L2 L 2 -norm. Extensive numerical experiments on a rotating BoseEinstein condensation and a rotating BEC in optical lattices are reported. Our numerical results show that the convergence rate of the SCM is exponential, and is independent of the collocation points we choose.
spectral-galerkin method grosspitaevskii equation legendre polynomials strong monotonicity condition error analysis