The Double Ramadan Group Accelerated Adomian Decomposition Method for Solving Nonlinear Partial Differential Equations

Articles in Press

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.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 07 June 2025

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History

  • Receive Date: 07 January 2025
  • Revise Date: 26 March 2025
  • Accept Date: 22 May 2025

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