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We extensively study the numerical accuracy of the well-known time splittingFourier spectral method for the approximation of singular solutions of theGross-Pitaevskii equation. In particular, we explore its capability ofpreserving a steady-state vortex solution, whose density profile isapproximated by a very accurate diagonal Pad\'e expansion of order 8, hereexplicitly derived for the first time. Although the Fourier spectral methodturns out to be only slightly more accurate than a time splitting finitedifference scheme, the former is reliable and efficient. Moreover, at apost-processing stage, it allows an accurate evaluation of the solution outsidegrid points, thus becoming particularly appealing when high resolution isneeded, such as in the study of quantum vortex interactions.

Reliability of the time splitting Fourier method for singular solutions in quantum fluids