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By implementing the exact density matrix for the rotating anisotropicharmonic trap, we derive a class of very fast and accurate fourth orderalgorithms for evolving the Gross-Pitaevskii equation in imaginary time. Suchfourth order algorithms are possible only with the use of {\it forward},positive time step factorization schemes. These fourth order algorithmsconverge at time-step sizes an order-of-magnitude larger than conventionalsecond order algorithms. Our use of time-dependent factorization schemesprovides a systematic way of devising algorithms for solving this type ofnonlinear equations.Comment: 14 pages with 3 figures, revised figures with the use of the Lambert  W-function for doing the self-consistent iterations. Published versio

Fourth-order algorithms for solving the imaginary-time Gross-Pitaevskii equation in a rotating anisotropic trap