Simulations of polydisperse multiphase flows must include the effects of particle breakage and aggregation, which requires the solution of the population balance equation (PBE). Therefore, the analysis of the existing numerical techniques to solve the PBE regarding their efficiency and accuracy is paramount to their implementation in CFD codes. This work focused on analyzing the three quadrature-based methods available in the literature (QMOM, DQMOM and PPDC) in terms of efficiency and accuracy and against the classical method of classes. Analytical solutions were used to derive test cases from dominant breakage to dominant aggregation. The methods were evaluated in terms of moment accuracy and convergence. The computational costs were evaluated for all cases. It was verified that PPDC has poor convergence and is not adequate. For all cases, the QMOM and DQMOM solutions presented similar accuracy, but the DQMOM was the most efficient method. (C) 2009 Elsevier Ltd. All rights reserved.