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<p>In this paper, we investigate the use of conformable approaches to numerically solve complex systems, namely the two-dimensional reaction–diffusion Brusselator model. In such models, the paper presents a new conformable residual series approach to deal with difficulties in solving nonlinear partial differential equations (PDEs). Also, we present a conformable iterative method, which is aimed to increase the computational efficiency and accuracy of the iterative solver. Using the characteristics of the conformable operator, we can develop a more stable method to truncate the dynamics of reaction–diffusion systems. The paper establishes, through theoretical evaluation and numerical experimentation, the efficacy of the conformable methods in enhancing rates of convergence and stability compare to the traditional techniques. The results in this paper will be useful in the future in both computational mathematics and theoretical biology, especially regarding modelling of biochemical reaction process and ecological dynamics.</p>

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Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Musawa Yahya Almusawa,
  • Mohammad Alqudah,
  • Hassan Almusawa,
  • Ahmad Shafee,
  • Adel Almarashi

摘要

In this paper, we investigate the use of conformable approaches to numerically solve complex systems, namely the two-dimensional reaction–diffusion Brusselator model. In such models, the paper presents a new conformable residual series approach to deal with difficulties in solving nonlinear partial differential equations (PDEs). Also, we present a conformable iterative method, which is aimed to increase the computational efficiency and accuracy of the iterative solver. Using the characteristics of the conformable operator, we can develop a more stable method to truncate the dynamics of reaction–diffusion systems. The paper establishes, through theoretical evaluation and numerical experimentation, the efficacy of the conformable methods in enhancing rates of convergence and stability compare to the traditional techniques. The results in this paper will be useful in the future in both computational mathematics and theoretical biology, especially regarding modelling of biochemical reaction process and ecological dynamics.