Local spectral time splitting method for first- and second-order partial differential equations
Journal of Computational Physics
Journal of Computational Physics
Dynamics of the center of mass in rotating Bose--Einstein condensates
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Complex Valued Spectral Hermite Approximations for the Actively Mode-Locked Laser
Journal of Scientific Computing
A fully adaptive reaction-diffusion integration scheme with applications to systems biology
Journal of Computational Physics
Journal of Computational Physics
A minimisation approach for computing the ground state of Gross-Pitaevskii systems
Journal of Computational Physics
High-order time-splitting Hermite and Fourier spectral methods
Journal of Computational Physics
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations
Computers & Mathematics with Applications
Journal of Scientific Computing
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A fourth-order time-splitting Laguerre--Hermite pseudospectral method is introduced for Bose--Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The method is explicit, time reversible, and time transverse invariant. It conserves the position density and is spectral accurate in space and fourth-order accurate in time. Moreover, the new method has two other important advantages: (i) it reduces a three-dimensional (3-D) problem with cylindrical symmetry to an effective two-dimensional (2-D) problem; (ii) it solves the problem in the whole space instead of in a truncated artificial computational domain. The method is applied to vector Gross--Pitaevskii equations (VGPEs) for multicomponent BECs. Extensive numerical tests are presented for the one-dimensional (1-D) GPE, the 2-D GPE with radial symmetry, the 3-D GPE with cylindrical symmetry, as well as 3-D VGPEs for two-component BECs, to show the efficiency and accuracy of the new numerical method.