Comparison of variational iteration and Adomian decomposition methods to solve growth, aggregation and aggregation-breakage equations

Abstract

In this work, semi-analytical approaches such as the Adomian decomposition method (ADM), and variational iteration method (VIM) are examined to solve the aggregation, aggregation-breakage and pure growth equations in series forms. The analytical and truncated series solutions are compared for the number density and various moments. The solutions produced using ADM and VIM are mathematically equal in the pure growth case and provide closed-form solutions for constant growth rate. Additionally, Optimal variational iteration method (OVIM) is implemented to solve the growth and aggregation equations, which reduces the error compared to ADM and VIM to some extent but increases the computational cost. Furthermore, in this work, we provide the ADM and VIM formulations for the coupled aggregation-breakage model. Various test cases of each problem are taken to justify the efficiency and accuracy of the series approximated methods. These observations are shown numerically by comparing the finite term series solutions with the exact solutions of number density and moments.