This work presents a new numerical scheme, the cell average technique, for solving population balance equations. The cell average technique (CAT) follows a two-step strategy, one to calculate average size of the newborn particles in a class and the other to assign them to neighboring nodes such that the properties of interest (moments) are exactly preserved. The main significance from the application point of view of the improved efficiency is that the CAT can be used as a tool for the calculation up to (or near to) the gelation point. Furthermore, the CAT has been applied to physically relevant problems and the results have been compared with the existing schemes. The CAT proposed in this work allows the convenience of using regular (linear, geometric- or equal-size) and irregular meshes. Furthermore, the CA scheme is consistent with the zeroth and first moments, the same procedure can be used to provide consistency with any two or more than two moments. A new approach for solving growth population balance equations is also presented. The growth process is treated as aggregation of existing particles in the disperse phase with some imaginary nuclei appearing form the continuous phase. Thus, the growth population balance equation is converted to the aggregation population balance equation. The aggregation rate is expressed in terms of the growth rate. Consequently, it becomes a trivial task to apply the CA technique to the transformed aggregation population balance equation. Further, a new concept for the coupling of different processes has been introduced. All processes including growth and nucleation have been solved using the CA technique by treating them uniformly. It has been demonstrated that the new approach of coupling is not only more accurate but also computationally less expensive. A substantial success of this coupling is observed for combined processes where growth is present because the coupling of growth with other processes has been a challenging task. The CAT has also been extended for solving two dimensional aggregation population balance equations.