Spectral collocation methods for the numerical solutions of Gross-Pitaevskii equation

• Main Authors: Shu-Hao Chang, 張書豪
• Other Authors: 簡澄陞
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/80755376529457953218

碩士 === 國立中興大學 === 應用數學系所 === 98 === We describe an efficient spectral collocation method (SCM) for the numerical solutions of the Gross-Pitaevskii equation (GPE), where the Legendre polynomials are used as the basis functions for the trial function space. We show that the SCM obtained in this way is equivalent to the spectral- Galerkin method (SGM) involving the Gauss-Legendre integration. The SCM is incorporated in the context of continuaton methods for computing energy levels and wave functions of the stationary state nonlinear Schr¨odinger equation. Numerical results on the Bose-Einstein condensates (BEC) in a periodic potential are reported.