To accurately predict aerosol dynamics in various systems, it is imperative to combine the governing equations for transport of momentum, mass and energy as well as reaction kinetics with an accurate procedure for solving the general dynamic equation (GDE). A generalized approach for solution of the GDE based on the discrete-sectional approach in presence of convective and molecular transport is presented. As computational efficiency is an important factor in realistic implementation of such a model, in Part-I of this two-part paper series an adaptive semi-implicit algorithm based on the concept of operating splitting is presented. It is shown that this algorithm is the method of choice for solving the GDE in presence or absence of convective transport based on a discrete-sectional approach. (C) 2003 Elsevier Ltd. All rights reserved.