Utilizing the Hybrid approach of the Ramadan group transform and accelerated Adomian method for solving nonlinear integro-differential equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 15، Issue 4 - شماره پیاپی 35، اسفند 2025، صفحه 1332-1360   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93657.1653

نویسندگان

M.A. Ramadan^{* 1}؛ M.M.A. Mansour²؛ H.S. Osheba²

¹Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Egypt.

²Department of basic science, Modern Academy of Computer Science and Management Technology in Maadi, Egypt.

چکیده

In this paper, we investigate the application of the combination of the Ramadan group transform and the accelerated Adomian polynomial method for solving integro-differential equations. Integro-differential equations arise in various fields such as physics, engineering, and biology, often modeling complex phenomena. The Ramadan group transform, known for its transformation properties and its ability to simplify computational complexities, is coupled with the accelerated Adomian polynomial method, which is an effective series expansion technique. This combination enhances the convergence and efficiency of solving nonlinear integro-differential equations that are difficult to handle using traditional methods. The paper demonstrates the utility of this hybrid approach through several test cases, comparing it with existing methods in terms of accuracy, computational efficiency, and convergence rate. 

کلیدواژه‌ها

Ramadan group transform (RGT)؛ Adomian polynomials؛ accelerated Adomian؛ Integro-differential equations؛ Accuracy

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