We develop a formulation of the Gross-Pitaevskii equation for the ultra-cold Bose gas in coordinates that adaptively scale with the system size during expansion, enabling numerical description of large spatial domains at fine resolution over long expansion times. The scaling dynamics is formulated for arbitrary confining potentials in terms of the stress tensor of the quantum fluid, a treatment that generalizes readily to non-contact interactions. The ideal gas, a cigar-shaped condensate in the Thomas-Fermi regime, and a linear superposition of wavepackets are evolved as applications of the scaling dynamics. We observe known scaling for a prolate BEC in the Thomas-Fermi regime, and identify a regime of linear self-similar expansion. Our results have implications for Bose-Einstein condensate experiments and matter-wave manipulation protocols at low temperature.