Collocation and Galerkin finite element algorithms are developed to solve the steady state population balance equation. Unlike previously proposed schemes, the algorithms are derived over an unsealed domain which permits accurate prediction of both the moments and the density distribution over domains large enough to reduce finite domain errors to negligibly small values. Simulations are performed for a large range of indices of aggregation for the two cases of i) aggregation alone and ii) combined growth and aggregation. In each case predictions are made of density distributions and the moments of the distributions, both of which are compared with analytical solutions.