We describe a model of dynamic Bose-Einstein condensates near a Feshbach resonance that is computationally feasible under assumptions of spherical or cylindrical symmetry. Simulations in spherical symmetry approximate the experimentally measured time to collapse of an unstably attractive condensate only when the molecular binding energy in the model is correct, demonstrating that quantum fluctuations and coupling between atoms and (un)bound pairs of atoms included in the model are the dominant mechanisms during collapse. Simulations of condensates with repulsive interactions find some quantitative disagreement, suggesting that pairing and quantum fluctuations are not the only significant factors for condensate loss or burst formation. Inclusion of three-body recombination was found to be inconsequential in all of our simulations, although we do not consider recent experiments [Phys. Rev. A 84, 033632 (2011)PLRAAN1050-294710.1103/PhysRevA.84.033632] conducted at over an order of magnitude higher density.