Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst
The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="...
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MDPI AG
2021-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/21/10423 |
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| author | Vivek Mani Tripathi Hari Mohan Srivastava Harendra Singh Chetan Swarup Sudhanshu Aggarwal |
| author_facet | Vivek Mani Tripathi Hari Mohan Srivastava Harendra Singh Chetan Swarup Sudhanshu Aggarwal |
| author_sort | Vivek Mani Tripathi |
| collection | DOAJ |
| description | The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi>the</mi><mo> </mo><mi>time</mi></mrow><mo> </mo><mi>t</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods. |
| first_indexed | 2024-03-09T04:38:49Z |
| format | Article |
| id | doaj.art-294d5a0f588442579a770807df7eccc9 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T04:38:49Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-294d5a0f588442579a770807df7eccc92023-12-03T13:23:41ZengMDPI AGApplied Sciences2076-34172021-11-0111211042310.3390/app112110423Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical BiocatalystVivek Mani Tripathi0Hari Mohan Srivastava1Harendra Singh2Chetan Swarup3Sudhanshu Aggarwal4Department of Engineering, Uttar Pradesh Textile Technology Institute, Kanpur 208001, IndiaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Post-Graduate College, Ghazipur 233001, IndiaDepartment of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 13316, Saudi ArabiaDepartment of Mathematics, National Post-Graduate College, Gorakhpur 273402, IndiaThe theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi>the</mi><mo> </mo><mi>time</mi></mrow><mo> </mo><mi>t</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods.https://www.mdpi.com/2076-3417/11/21/10423reaction–diffusion modelsdynamical system involving the Lane–Emden-type equationsspherical catalystLane–Emden problemspherical biocatalystspectral collocation method |
| spellingShingle | Vivek Mani Tripathi Hari Mohan Srivastava Harendra Singh Chetan Swarup Sudhanshu Aggarwal Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst Applied Sciences reaction–diffusion models dynamical system involving the Lane–Emden-type equations spherical catalyst Lane–Emden problem spherical biocatalyst spectral collocation method |
| title | Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst |
| title_full | Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst |
| title_fullStr | Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst |
| title_full_unstemmed | Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst |
| title_short | Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst |
| title_sort | mathematical analysis of non isothermal reaction diffusion models arising in spherical catalyst and spherical biocatalyst |
| topic | reaction–diffusion models dynamical system involving the Lane–Emden-type equations spherical catalyst Lane–Emden problem spherical biocatalyst spectral collocation method |
| url | https://www.mdpi.com/2076-3417/11/21/10423 |
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