In this article, we propose a simple and effective methods to resolve the reaction diffusion equation for facilitated emigration of planar electrode in a steady state non-linear process that arises in the context of the electroactive polymer film. The mathematical modeling presented here suggest a substrate and an immobilized catalyst form a complex. By applying the two effective analytical approach namely Homotopy Analysis Method and Exp-Function Method, an approximate analytical expression for the substrate concentration for planar electrode is established. Moreover, the analytical approach of the current for the experimental outcomes is established. The efficiency of the methods is demonstrated by contrasting the numerical simulation with the Analytical findings. The derived analytical outcomes are compared with numerical data which is obtained by using Matlab software and it is transpires that they correspond adequately. Also the comparison of computational outcomes with dimensionless concentration of planar electrode substrate in its analytical representation established in table. In these table results depicts for different amount of reaction and diffusion parameters our new result agree rather well with the numerical findings. The error percentage of our results employing Homotopy Analysis Method and Exp-Function Method with numerical results presented. The solution is also graphically presented. It provides a satisfactory agreement for all parameter setting under comparison.
| Published in | Applied and Computational Mathematics (Volume 13, Issue 6) |
| DOI | 10.11648/j.acm.20241306.13 |
| Page(s) | 236-244 |
| 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), 2024. Published by Science Publishing Group |
Mathematical Modeling, Nonlinear Differential Equation, Reaction Diffusion Equation, Electroactive Polymer Film, Homotopy Analysis Method, Exp-Function Method
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APA Style
Andiappan, U., Rajagopal, S. (2024). Mathematical Modeling of Reaction Diffusion Equation for Facilitated Emigration of Planar Electrode in a Non-Linear Process at Electroactive Polymer Film. Applied and Computational Mathematics, 13(6), 236-244. https://doi.org/10.11648/j.acm.20241306.13
ACS Style
Andiappan, U.; Rajagopal, S. Mathematical Modeling of Reaction Diffusion Equation for Facilitated Emigration of Planar Electrode in a Non-Linear Process at Electroactive Polymer Film. Appl. Comput. Math. 2024, 13(6), 236-244. doi: 10.11648/j.acm.20241306.13
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Download@article{10.11648/j.acm.20241306.13,
author = {Uma Andiappan and Swaminathan Rajagopal},
title = {Mathematical Modeling of Reaction Diffusion Equation for Facilitated Emigration of Planar Electrode in a Non-Linear Process at Electroactive Polymer Film
},
journal = {Applied and Computational Mathematics},
volume = {13},
number = {6},
pages = {236-244},
doi = {10.11648/j.acm.20241306.13},
url = {https://doi.org/10.11648/j.acm.20241306.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20241306.13},
abstract = {In this article, we propose a simple and effective methods to resolve the reaction diffusion equation for facilitated emigration of planar electrode in a steady state non-linear process that arises in the context of the electroactive polymer film. The mathematical modeling presented here suggest a substrate and an immobilized catalyst form a complex. By applying the two effective analytical approach namely Homotopy Analysis Method and Exp-Function Method, an approximate analytical expression for the substrate concentration for planar electrode is established. Moreover, the analytical approach of the current for the experimental outcomes is established. The efficiency of the methods is demonstrated by contrasting the numerical simulation with the Analytical findings. The derived analytical outcomes are compared with numerical data which is obtained by using Matlab software and it is transpires that they correspond adequately. Also the comparison of computational outcomes with dimensionless concentration of planar electrode substrate in its analytical representation established in table. In these table results depicts for different amount of reaction and diffusion parameters our new result agree rather well with the numerical findings. The error percentage of our results employing Homotopy Analysis Method and Exp-Function Method with numerical results presented. The solution is also graphically presented. It provides a satisfactory agreement for all parameter setting under comparison.
},
year = {2024}
}
TY - JOUR T1 - Mathematical Modeling of Reaction Diffusion Equation for Facilitated Emigration of Planar Electrode in a Non-Linear Process at Electroactive Polymer Film AU - Uma Andiappan AU - Swaminathan Rajagopal Y1 - 2024/12/30 PY - 2024 N1 - https://doi.org/10.11648/j.acm.20241306.13 DO - 10.11648/j.acm.20241306.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 236 EP - 244 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20241306.13 AB - In this article, we propose a simple and effective methods to resolve the reaction diffusion equation for facilitated emigration of planar electrode in a steady state non-linear process that arises in the context of the electroactive polymer film. The mathematical modeling presented here suggest a substrate and an immobilized catalyst form a complex. By applying the two effective analytical approach namely Homotopy Analysis Method and Exp-Function Method, an approximate analytical expression for the substrate concentration for planar electrode is established. Moreover, the analytical approach of the current for the experimental outcomes is established. The efficiency of the methods is demonstrated by contrasting the numerical simulation with the Analytical findings. The derived analytical outcomes are compared with numerical data which is obtained by using Matlab software and it is transpires that they correspond adequately. Also the comparison of computational outcomes with dimensionless concentration of planar electrode substrate in its analytical representation established in table. In these table results depicts for different amount of reaction and diffusion parameters our new result agree rather well with the numerical findings. The error percentage of our results employing Homotopy Analysis Method and Exp-Function Method with numerical results presented. The solution is also graphically presented. It provides a satisfactory agreement for all parameter setting under comparison. VL - 13 IS - 6 ER -
PG & Research Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India
PG & Research Department of Mathematics, Vidhyaa Giri College of Arts and Science (Affiliated to Alagappa University), Puduvayal, India
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