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A spectral collocation method for a rotating Bose–Einstein condensation in optical lattices |
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| Authors: | Z.-C. Li S.-Y. Chen C.-S. Chien H.-S. Chen |
| Affiliation: | aDepartment of Applied Mathematics, Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan;bDepartment of Applied Mathematics, Chung Hua University, Hsin-Chu 30012, Taiwan;cDepartment of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan;dDepartment of Computer Science and Information Engineering, Ching-Yun University, Jhongli 32097, Taiwan |
| Abstract: | 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 H1-norm and L2-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. |
| Keywords: | Spectral-Galerkin method Gross&ndash Pitaevskii equation Legendre polynomials Strong monotonicity condition Error analysis |
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