Analytical approach for solving population balances: A homotopy perturbation method

Gurmeet Kaur, Randhir Singh, Mehakpreet Singh, Jitendra Kumar, Themis Matsoukas

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


In the present work, a new approach is proposed for finding the analytical solution of population balances for aggregation and fragmentation process. This approach is relying on the idea of the 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. In addition, the analytical solution to two new kernels (the power-law kernel in fragmentation and the Ruckenstein/Pulvermacher kernel in aggregation) are also introduced.

Original languageEnglish (US)
Article number385201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number38
StatePublished - Aug 26 2019

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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