Analytical Approach For Solving Population Balances: A Homotopy Perturbation Method

TL;DR

This paper introduces a novel analytical method using Homotopy Perturbation Method to solve population balance equations, avoiding common numerical issues and providing accurate solutions without linearization or discretization.

Contribution

It presents a new analytical approach based on HPM for solving population balances, which enhances stability and accuracy over traditional numerical methods.

Findings

Successfully applied to examples including Austin's kernel

Avoids numerical stability problems common in other methods

Provides series solutions with easily computable components

Abstract

In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel available in literature are examined to demonstrate the accuracy and applicability of the proposed method.