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<p>This paper presents advanced iterative methods based on the Adomian Decomposition Method (ADM) for efficiently solving complex nonlinear equations that frequently arise in scientific and engineering applications. Recognizing the limitations of traditional techniques, such as slow convergence and high computational cost, we develop new third-, fourth-, and sixth-order iterative schemes to significantly improve convergence behavior and solution accuracy. The novelty of this work lies in the extension of the classical ADM framework to construct higher-order methods without resorting to linearization or perturbation techniques. To validate the effectiveness of the proposed methods, a detailed comparative study is conducted against existing higher-order iterative approaches. The comparison is made in terms of convergence order, number of iterations, computational effort, and accuracy through a series of numerical examples drawn from real-world models in population dynamics, fluid flow, and chemical kinetics. The results clearly demonstrate that the new methods outperform their counterparts, offering faster convergence and reduced computational costs while maintaining high accuracy. These advances have substantial potential to improve simulations and predictive modeling in various fields, including physics, engineering, environmental science, and biomedical applications.</p>

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Efficient nonlinear numerical techniques for solving complex scientific systems using Adomian decomposition

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Muhammad Raza,
  • Urooj Suleman,
  • Najma Abdul Rehman

摘要

This paper presents advanced iterative methods based on the Adomian Decomposition Method (ADM) for efficiently solving complex nonlinear equations that frequently arise in scientific and engineering applications. Recognizing the limitations of traditional techniques, such as slow convergence and high computational cost, we develop new third-, fourth-, and sixth-order iterative schemes to significantly improve convergence behavior and solution accuracy. The novelty of this work lies in the extension of the classical ADM framework to construct higher-order methods without resorting to linearization or perturbation techniques. To validate the effectiveness of the proposed methods, a detailed comparative study is conducted against existing higher-order iterative approaches. The comparison is made in terms of convergence order, number of iterations, computational effort, and accuracy through a series of numerical examples drawn from real-world models in population dynamics, fluid flow, and chemical kinetics. The results clearly demonstrate that the new methods outperform their counterparts, offering faster convergence and reduced computational costs while maintaining high accuracy. These advances have substantial potential to improve simulations and predictive modeling in various fields, including physics, engineering, environmental science, and biomedical applications.