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The Gross-Pitaevskii equation with white noise in time perturbations of theharmonic potential is considered. In this article we define a Crank-Nicolsonscheme based on a spectral discretization and we show the convergence of thisscheme in the case of cubic non-linearity and when the exact solution isuniquely defined and global in time. We prove that the strong order ofconvergence in probability is at least one.

Numerical analysis of the Gross-Pitaevskii Equation with a randomly varying potential in time