Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method

Chinnathambi Kartheeswari; Rajagopal Swaminathan

doi:doi:10.11648/j.mma.20261102.12

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Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method

Chinnathambi Kartheeswari, Rajagopal Swaminathan^*

Published in Mathematical Modelling and Applications (Volume 11, Issue 2)

Received: 21 July 2026 Accepted: 3 August 2026 Published: 5 September 2026

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Abstract

The present study develops a nonlinear mathematical model to investigate the kinetic behavior of autocatalytic halide anion reactions, which exhibit complex dynamic characteristics due to autocatalysis and feedback-driven reaction mechanisms. Such reactions play a significant role in nonlinear chemical kinetics and provide valuable insights into the behavior of reaction systems under varying kinetic conditions. The primary objective of this work is to formulate the governing nonlinear reaction--diffusion equations based on the fundamental principles of reaction kinetics and to derive approximate analytical solutions using the Taylor Series Method (TSM). The proposed analytical approach provides an efficient and systematic framework for approximating the concentration profiles of the reacting species while accurately capturing the nonlinear dynamics of the reaction system within its domain of convergence. The analytical solutions are employed to investigate the influence of various kinetic parameters on the concentration profiles, thereby providing a deeper understanding of the reaction mechanism and system behavior. To validate the effectiveness and accuracy of the proposed method, the analytical results are compared with numerical solutions obtained using MATLAB, demonstrating excellent agreement over the parameter ranges considered. Furthermore, numerical simulations are performed to visualize the concentration profiles of the reacting species and to illustrate the effects of different kinetic parameters on the system dynamics. The close agreement between the analytical and numerical results confirms the reliability, accuracy, and computational efficiency of the Taylor Series Method for solving nonlinear reaction models. The mathematical analysis presented in this study enhances the understanding of autocatalytic halide anion reaction kinetics and establishes a reliable analytical framework for investigating similar nonlinear reaction--diffusion systems. The proposed methodology provides compact, accurate, and computationally efficient analytical approximations that can be readily applied, validated, and extended to a broad class of nonlinear reaction--diffusion and chemical kinetic models.

Published in	Mathematical Modelling and Applications (Volume 11, Issue 2)
DOI	10.11648/j.mma.20261102.12
Page(s)	41-52
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Autocatalytic Halide Anion Reaction, Nonlinear Equations, Mathematical Modeling, Taylor Series Method

References

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Kartheeswari, C., Swaminathan, R. (2026). Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Mathematical Modelling and Applications, 11(2), 41-52. https://doi.org/10.11648/j.mma.20261102.12

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ACS Style

Kartheeswari, C.; Swaminathan, R. Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Math. Model. Appl. 2026, 11(2), 41-52. doi: 10.11648/j.mma.20261102.12

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AMA Style

Kartheeswari C, Swaminathan R. Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Math Model Appl. 2026;11(2):41-52. doi: 10.11648/j.mma.20261102.12

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@article{10.11648/j.mma.20261102.12,
  author = {Chinnathambi Kartheeswari and Rajagopal Swaminathan},
  title = {Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method},
  journal = {Mathematical Modelling and Applications},
  volume = {11},
  number = {2},
  pages = {41-52},
  doi = {10.11648/j.mma.20261102.12},
  url = {https://doi.org/10.11648/j.mma.20261102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20261102.12},
  abstract = {The present study develops a nonlinear mathematical model to investigate the kinetic behavior of autocatalytic halide anion reactions, which exhibit complex dynamic characteristics due to autocatalysis and feedback-driven reaction mechanisms. Such reactions play a significant role in nonlinear chemical kinetics and provide valuable insights into the behavior of reaction systems under varying kinetic conditions. The primary objective of this work is to formulate the governing nonlinear reaction--diffusion equations based on the fundamental principles of reaction kinetics and to derive approximate analytical solutions using the Taylor Series Method (TSM). The proposed analytical approach provides an efficient and systematic framework for approximating the concentration profiles of the reacting species while accurately capturing the nonlinear dynamics of the reaction system within its domain of convergence. The analytical solutions are employed to investigate the influence of various kinetic parameters on the concentration profiles, thereby providing a deeper understanding of the reaction mechanism and system behavior. To validate the effectiveness and accuracy of the proposed method, the analytical results are compared with numerical solutions obtained using MATLAB, demonstrating excellent agreement over the parameter ranges considered. Furthermore, numerical simulations are performed to visualize the concentration profiles of the reacting species and to illustrate the effects of different kinetic parameters on the system dynamics. The close agreement between the analytical and numerical results confirms the reliability, accuracy, and computational efficiency of the Taylor Series Method for solving nonlinear reaction models. The mathematical analysis presented in this study enhances the understanding of autocatalytic halide anion reaction kinetics and establishes a reliable analytical framework for investigating similar nonlinear reaction--diffusion systems. The proposed methodology provides compact, accurate, and computationally efficient analytical approximations that can be readily applied, validated, and extended to a broad class of nonlinear reaction--diffusion and chemical kinetic models.},
 year = {2026}
}

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TY  - JOUR
T1  - Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method
AU  - Chinnathambi Kartheeswari
AU  - Rajagopal Swaminathan
Y1  - 2026/09/05
PY  - 2026
N1  - https://doi.org/10.11648/j.mma.20261102.12
DO  - 10.11648/j.mma.20261102.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 41
EP  - 52
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20261102.12
AB  - The present study develops a nonlinear mathematical model to investigate the kinetic behavior of autocatalytic halide anion reactions, which exhibit complex dynamic characteristics due to autocatalysis and feedback-driven reaction mechanisms. Such reactions play a significant role in nonlinear chemical kinetics and provide valuable insights into the behavior of reaction systems under varying kinetic conditions. The primary objective of this work is to formulate the governing nonlinear reaction--diffusion equations based on the fundamental principles of reaction kinetics and to derive approximate analytical solutions using the Taylor Series Method (TSM). The proposed analytical approach provides an efficient and systematic framework for approximating the concentration profiles of the reacting species while accurately capturing the nonlinear dynamics of the reaction system within its domain of convergence. The analytical solutions are employed to investigate the influence of various kinetic parameters on the concentration profiles, thereby providing a deeper understanding of the reaction mechanism and system behavior. To validate the effectiveness and accuracy of the proposed method, the analytical results are compared with numerical solutions obtained using MATLAB, demonstrating excellent agreement over the parameter ranges considered. Furthermore, numerical simulations are performed to visualize the concentration profiles of the reacting species and to illustrate the effects of different kinetic parameters on the system dynamics. The close agreement between the analytical and numerical results confirms the reliability, accuracy, and computational efficiency of the Taylor Series Method for solving nonlinear reaction models. The mathematical analysis presented in this study enhances the understanding of autocatalytic halide anion reaction kinetics and establishes a reliable analytical framework for investigating similar nonlinear reaction--diffusion systems. The proposed methodology provides compact, accurate, and computationally efficient analytical approximations that can be readily applied, validated, and extended to a broad class of nonlinear reaction--diffusion and chemical kinetic models.
VL  - 11
IS  - 2
ER  -

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Chinnathambi Kartheeswari

Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India

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Rajagopal Swaminathan

Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India

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APA Style

Kartheeswari, C., Swaminathan, R. (2026). Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Mathematical Modelling and Applications, 11(2), 41-52. https://doi.org/10.11648/j.mma.20261102.12

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ACS Style

Kartheeswari, C.; Swaminathan, R. Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Math. Model. Appl. 2026, 11(2), 41-52. doi: 10.11648/j.mma.20261102.12

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AMA Style

Kartheeswari C, Swaminathan R. Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method. Math Model Appl. 2026;11(2):41-52. doi: 10.11648/j.mma.20261102.12

Copy | Download

@article{10.11648/j.mma.20261102.12,
  author = {Chinnathambi Kartheeswari and Rajagopal Swaminathan},
  title = {Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method},
  journal = {Mathematical Modelling and Applications},
  volume = {11},
  number = {2},
  pages = {41-52},
  doi = {10.11648/j.mma.20261102.12},
  url = {https://doi.org/10.11648/j.mma.20261102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20261102.12},
  abstract = {The present study develops a nonlinear mathematical model to investigate the kinetic behavior of autocatalytic halide anion reactions, which exhibit complex dynamic characteristics due to autocatalysis and feedback-driven reaction mechanisms. Such reactions play a significant role in nonlinear chemical kinetics and provide valuable insights into the behavior of reaction systems under varying kinetic conditions. The primary objective of this work is to formulate the governing nonlinear reaction--diffusion equations based on the fundamental principles of reaction kinetics and to derive approximate analytical solutions using the Taylor Series Method (TSM). The proposed analytical approach provides an efficient and systematic framework for approximating the concentration profiles of the reacting species while accurately capturing the nonlinear dynamics of the reaction system within its domain of convergence. The analytical solutions are employed to investigate the influence of various kinetic parameters on the concentration profiles, thereby providing a deeper understanding of the reaction mechanism and system behavior. To validate the effectiveness and accuracy of the proposed method, the analytical results are compared with numerical solutions obtained using MATLAB, demonstrating excellent agreement over the parameter ranges considered. Furthermore, numerical simulations are performed to visualize the concentration profiles of the reacting species and to illustrate the effects of different kinetic parameters on the system dynamics. The close agreement between the analytical and numerical results confirms the reliability, accuracy, and computational efficiency of the Taylor Series Method for solving nonlinear reaction models. The mathematical analysis presented in this study enhances the understanding of autocatalytic halide anion reaction kinetics and establishes a reliable analytical framework for investigating similar nonlinear reaction--diffusion systems. The proposed methodology provides compact, accurate, and computationally efficient analytical approximations that can be readily applied, validated, and extended to a broad class of nonlinear reaction--diffusion and chemical kinetic models.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Nonlinear Mathematical Modelling of Autocatalytic Redox-mediated Electroreduction of Halogen Oxoanions Using Taylor Series Method
AU  - Chinnathambi Kartheeswari
AU  - Rajagopal Swaminathan
Y1  - 2026/09/05
PY  - 2026
N1  - https://doi.org/10.11648/j.mma.20261102.12
DO  - 10.11648/j.mma.20261102.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 41
EP  - 52
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20261102.12
AB  - The present study develops a nonlinear mathematical model to investigate the kinetic behavior of autocatalytic halide anion reactions, which exhibit complex dynamic characteristics due to autocatalysis and feedback-driven reaction mechanisms. Such reactions play a significant role in nonlinear chemical kinetics and provide valuable insights into the behavior of reaction systems under varying kinetic conditions. The primary objective of this work is to formulate the governing nonlinear reaction--diffusion equations based on the fundamental principles of reaction kinetics and to derive approximate analytical solutions using the Taylor Series Method (TSM). The proposed analytical approach provides an efficient and systematic framework for approximating the concentration profiles of the reacting species while accurately capturing the nonlinear dynamics of the reaction system within its domain of convergence. The analytical solutions are employed to investigate the influence of various kinetic parameters on the concentration profiles, thereby providing a deeper understanding of the reaction mechanism and system behavior. To validate the effectiveness and accuracy of the proposed method, the analytical results are compared with numerical solutions obtained using MATLAB, demonstrating excellent agreement over the parameter ranges considered. Furthermore, numerical simulations are performed to visualize the concentration profiles of the reacting species and to illustrate the effects of different kinetic parameters on the system dynamics. The close agreement between the analytical and numerical results confirms the reliability, accuracy, and computational efficiency of the Taylor Series Method for solving nonlinear reaction models. The mathematical analysis presented in this study enhances the understanding of autocatalytic halide anion reaction kinetics and establishes a reliable analytical framework for investigating similar nonlinear reaction--diffusion systems. The proposed methodology provides compact, accurate, and computationally efficient analytical approximations that can be readily applied, validated, and extended to a broad class of nonlinear reaction--diffusion and chemical kinetic models.
VL  - 11
IS  - 2
ER  -

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