The use of moment methods for simulation of aerosol settling and diffusion phenomena in which the settling velocity and diffusion coefficient are functions of the size of the particles leads to difficult computational problems, especially if the moment equations need to be closed. In this study, a simple one dimensional problem of aerosol diffusion and gravitational settling is carried out using quadrature method of moments (QMOM) and the direct quadrature method of moments (DQMOM). Analytical solutions can be obtained for the number density function, and issues related to the integration of the solutions to get the moments are discussed. Comparison of the solutions of the moment equations to the moments obtained from the analytical solutions reveals that solutions depend on the initial choice of moments. Results also indicate that the proper choice of moments of the initial number density function may be a significant factor in obtaining more accurate solutions from QMOM or DQMOM. (C) 2005 Elsevier Ltd. All rights reserved.