The simple shearing of a suspension of charge-stabilized, colloidal particles close to the melting line is investigated by massively parallel, nonequilibrium Brownian dynamics (NEBD) simulation. The suspension undergoes a discontinuous transition from a distorted fluid structure to an ordered "string" phase. Comparisons between simulations of 43 000, 4725 particles, and previous NEED work on less than or equal to 500 particles proves that shear-induced ordering is not all artifact of the small system sizes. We also show that the shear-rate dependence of the rheological properties obtained from NEED is different than those obtained from nonequilibrium molecular dynamics (NEMD), a consequence of the solvent damping not being present in NEMD. The validity of the Ree-Eyring model for viscosity and the stress-optic law for colloids are tested. Further, a type of generalized Stokes-Einstein relationship is discovered for systems under shear.