We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schrödinger equation used to simulate the dynamics of  Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.

This article has been published in The Physical Review E 67, 046706 (2003) and may be found at http://publish.aps.org/abstract/PRE/v67/e046706.

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