A spectral collocation method for a rotating Bose–Einstein 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 Bose–Einstein condensation (BEC) and a rotating BEC in optical lattices. We apply the Lagrange interpolants using the Legendre–Gauss–Lobatto points to derive error bounds for the SCM. The optimal error bounds are derived for both H1H1-norm and L2L2-norm. Extensive numerical experiments on a rotating Bose–Einstein 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.