Pinar, Zehra2024-10-292024-10-2920221686-0209https://hdl.handle.net/20.500.11776/12652We propose a semi-analytical method to solve partial integro-differential equations with ini-tial/boundary conditions. This work investigates the semi-analytical solutions of the population balance models (PBMs) for the batch systems. The comparison of obtained solutions with the known exact solutions is given to show the effectiveness of the proposed method. The proposed method is very useful, reliable, and flexible; also, the solutions can play key role population balance models in engineering and science which are different kinds of partial integro-differential equations. © 2022 by TJM. All rights reserved.eninfo:eu-repo/semantics/closedAccessbatch systemsdroplet breakuppopulation balance modelsemi-analytical solutionsArticle2025455552-s2.0-85133654266Q4