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Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap

Siu A. Chin·Eckhard Krotscheck
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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.

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Siu A. Chin, Eckhard Krotscheck. 2005-10-03. Fourth-Order Algorithms for Solving the Imaginary Time Gross-Pitaevskii Equation in a Rotating Anisotropic Trap. https://doi.org/10.1103/physreve.72.036705

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