Adomian Decomposition Method for Population Balance Equations and the Study of Convergence

Abstract

The Adomian decomposition method has received much attention in recent years in applied mathematics in general and in the area of series solutions in particular. It is an effective technique for the analytical solution of a wide class of dynamical systems. The population balance equation (PBE) has been used to model a variety of particulate Process. However, only a few cases where analytical solutions for the breakage/coalescence process exist, most of these solutions are for the spatially homogeneous system. The main objective of this thesis is to derive analytical solutions of spatially inhomogeneous PBE For breakage/ coalescence processes using the Adomian decomposition method which uses a specific kind of polynomials named ”Adomian’s polynomials” to decompose the nonlinear part of such equation. The results obtained indicate that the ADM avoids numerical stability problems that often characterize general numerical techniques in this area.