Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator.
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| Title: | Mathematical analysis of the reaction–diffusion Brusselator system within conformable operator. |
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| Authors: | Almusawa, Musawa Yahya1 (AUTHOR), Alqudah, Mohammad2 (AUTHOR), Almusawa, Hassan1 (AUTHOR), Shafee, Ahmad3 (AUTHOR) as.zada@paaet.edu.kw, Almarashi, Adel1 (AUTHOR) |
| Source: | Pramana: Journal of Physics. Jun2026, Vol. 100 Issue 2, p1-25. 25p. |
| Subjects: | Reaction-diffusion equations, Partial differential equations, Iterative methods (Mathematics), Computational mathematics, Biomathematics, Numerical analysis |
| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 03044289 |
| DOI: | 10.1007/s12043-025-03041-z |
