An improved solution based on Temimi–Ansari method for coagulation and coupled coagulation fragmentation equations

Abstract

This article introduces a novel semi-analytical solution for the aggregation equation utilizing the Temimi–Ansari Method in conjunction with Pade approximants. The methodology is further adapted to address coupled aggregation–fragmentation equations, owing to the demonstrated accuracy and efficiency in handling aggregation equations. The study conducts a comprehensive convergence analysis and establishes error bounds for the proposed method. Various test cases are examined to demonstrate the efficacy of the methodology. Comparative assessments between approximated and exact solutions reveal a noteworthy concordance over an extended temporal domain, thereby addressing a substantial void in the existing literature. In the study conducted by Arora et al. (J Comput Sci 67:101973, 2023), it is noteworthy to highlight that the variational iteration method demonstrates superior quantitative accuracy in comparison to both Adomian decomposition and homotopy perturbation methods. Additionally, it is observed that the Temimi–Ansari Method yields comparable accuracy to the variational iteration method but requires less computational time. Simultaneously, the Temimi–Ansari Method, when coupled with Pade approximants, exhibits superior quantitative accuracy compared to the variational iteration method. As a result, the presented article showcases a notable advancement in solutions, surpassing the accuracy of prevailing semi-analytical solutions documented in the literature. The discrepancies between the exact and the derived series solutions are presented through graphical plots and tables, affirming the applicability and precision of the proposed approach.