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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17610
Title: Elzaki projected differential transform method for multi-dimensional aggregation and combined aggregation-breakage equations
Authors: Kumar, Rajesh
Keywords: Mathematics
Population balance equation
Aggregation-breakage
Semi-analytical techniques
Elzaki transformation
Projected differential transformation
Issue Date: Jan-2024
Publisher: Elsevier
Abstract: Numerous real-world fields, including planetary science, bio-pharmaceutical, chemical study, food processing industry, and many more are profoundly impacted by population balance equations. Model complexity limits the analytical investigations to a few aggregation-breakage parameters, although various numerical and semi-analytical schemes are available. This article proposes a new semi-analytical approach, the Elzaki integral transform as a pre-treatment to reinforce domain decomposition for better accuracy and convergence, in conjunction with the projected differential transform method for finding the closed form or approximated series solutions for non-linear aggregation, aggregation-breakage, and multi-dimensional aggregation equations. The technique’s key benefit over traditional numerical methods is its ability to solve linear or non-linear differential equations directly without discretization or linearization. Theoretical convergence analysis and error estimates of series solutions for both one and two dimensional aggregation models are of particular interest. Finally, several numerical examples of aggregation, aggregation-breakage, and two dimensional aggregation equations are taken to validate the accuracy of the proposed method by comparing numerical simulations with exact solutions. Interestingly, we have obtained closed form solutions for the pure aggregation equation when considering constant and product aggregation kernels. Additionally, error tables and graphs help to highlight the method’s innovative nature
URI: https://www.sciencedirect.com/science/article/pii/S1877750324000048
http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17610
Appears in Collections:Department of Mathematics

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