The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations

Ramadan, Mohamed A.; Mansour, Mariam M. A.; El-Shazly, Naglaa A.; Osheba, Heba A.

doi:10.22034/cmde.2025.65368.3000

The double Ramadan group accelerated the Adomian decomposition method for solving nonlinear partial differential equations

Document Type : Research Paper

Authors

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

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

10.22034/cmde.2025.65368.3000

Abstract

This paper investigates an advanced method for solving partial differential equations (PDEs) by integrating the Double Ramadan Group Transform (DRGT) with a faster version of the Adomian Decomposition Method (ADM). Initially, the DRGT is applied to transform the PDEs, which simplifies the management of boundary conditions and linear elements. The resulting transformed PDEs are subsequently solved using the enhanced ADM, which is specially tailored to efficiently handle the nonlinear terms that typically make solutions more difficult. The acceleration of the ADM is achieved by utilizing improved decomposition techniques and optimized series expansion methods, leading to significant gains in both the speed of convergence and the accuracy in addressing nonlinearities. The effectiveness of this combined approach is illustrated through several examples involving complex PDEs with challenging nonlinear aspects. The findings demonstrate significant improvements in computational efficiency and solution accuracy, underscoring the potential of this method for solving a wide variety of PDE problems in scientific and engineering applications.

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