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

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.

کلیدواژه ها:

Ramadan group transform (RGT) ، Adomian polynomials ، Accelerated Adomian ، Integro-differential equations ، Accuracy