The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
SIAM Journal on Numerical Analysis
Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
SIAM Journal on Scientific Computing
Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains
SIAM Journal on Numerical Analysis
A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
SIAM Journal on Scientific Computing
A new generalized Laguerre spectral approximation and its applications
Journal of Computational and Applied Mathematics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient Flow
SIAM Journal on Scientific Computing
Journal of Computational Physics
A New Sobolev Gradient Method for Direct Minimization of the Gross-Pitaevskii Energy with Rotation
SIAM Journal on Scientific Computing
The spectral methods for parabolic Volterra integro-differential equations
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
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A generalized-Laguerre-Hermite pseudospectral method is proposed for computing symmetric and central vortex states in Bose-Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The new method is based on the properly scaled generalized-Laguerre-Hermite functions and a normalized gradient flow. It enjoys three important advantages: (i) it reduces a three-dimensional (3D) problem with cylindrical symmetry into an effective two-dimensional (2D) problem; (ii) it solves the problem in the whole space instead of in a truncated artificial computational domain and (iii) it is spectrally accurate. Extensive numerical results for computing symmetric and central vortex states in BECs are presented for one-dimensional (1D) BEC, 2D BEC with radial symmetry and 3D BEC with cylindrical symmetry.