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<p>In this study, we address the mathematical modeling and solution of a non-isothermal reaction diffusion model involving a spherical biocatalyst and catalyst. The system is shaped by an intricate balance between diffusion processes and chemical reactions. We investigate the Lane-Emden equation as governing equation of the model, which accounts for the spatial distribution of reactants and products. To tackle the singularity challenges associated with this dynamic system, we employ the semi-analytical approach, namely Differential Transform Method (DTM), enhanced by Padé approximation. In order to establish the reliability and effectiveness of proposed scheme, we conduct a comprehensive comparison with solutions available in the existing literature. Furthermore, a comprehensive investigation of sensitivity of the parameters is also conducted. Combining DTM and Padé approximation offers a promising robust computational technique for further study in the field of mathematical modeling of chemical and biological processes affected by singularities.</p>

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Dynamic Modeling and Parameter Sensitivity in Singular Non-Isothermal Reaction-Diffusion Systems: A DTM-Padé Solution for Spherical Catalysts

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月10日

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  • Yogeshwari F. Patel,
  • Mohammad Izadi

摘要

In this study, we address the mathematical modeling and solution of a non-isothermal reaction diffusion model involving a spherical biocatalyst and catalyst. The system is shaped by an intricate balance between diffusion processes and chemical reactions. We investigate the Lane-Emden equation as governing equation of the model, which accounts for the spatial distribution of reactants and products. To tackle the singularity challenges associated with this dynamic system, we employ the semi-analytical approach, namely Differential Transform Method (DTM), enhanced by Padé approximation. In order to establish the reliability and effectiveness of proposed scheme, we conduct a comprehensive comparison with solutions available in the existing literature. Furthermore, a comprehensive investigation of sensitivity of the parameters is also conducted. Combining DTM and Padé approximation offers a promising robust computational technique for further study in the field of mathematical modeling of chemical and biological processes affected by singularities.