Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap
arXiv:cond-mat/0504270 · doi:10.1103/PhysRevE.72.036705
Abstract
By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth order algorithms are possible only with the use of {\it forward}, positive time step factorization schemes. These fourth order algorithms converge at time-step sizes an order-of-magnitude larger than conventional second order algorithms. Our use of time-dependent factorization schemes provides a systematic way of devising algorithms for solving this type of nonlinear equations.
14 pages with 3 figures, revised figures with the use of the Lambert W-function for doing the self-consistent iterations. Published version
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