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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Autores principales:	Vivek Mani Tripathi, Hari Mohan Srivastava, Harendra Singh, Chetan Swarup, Sudhanshu Aggarwal
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	reaction–diffusion models dynamical system involving the Lane–Emden-type equations spherical catalyst Lane–Emden problem spherical biocatalyst spectral collocation method Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/294d5a0f588442579a770807df7eccc9
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id	oai:doaj.org-article:294d5a0f588442579a770807df7eccc9
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spelling	oai:doaj.org-article:294d5a0f588442579a770807df7eccc92021-11-11T15:24:09ZMathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst10.3390/app1121104232076-3417https://doaj.org/article/294d5a0f588442579a770807df7eccc92021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10423https://doaj.org/toc/2076-3417The 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.Vivek Mani TripathiHari Mohan SrivastavaHarendra SinghChetan SwarupSudhanshu AggarwalMDPI AGarticlereaction–diffusion modelsdynamical system involving the Lane–Emden-type equationsspherical catalystLane–Emden problemspherical biocatalystspectral collocation methodTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10423, p 10423 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	reaction–diffusion models dynamical system involving the Lane–Emden-type equations spherical catalyst Lane–Emden problem spherical biocatalyst spectral collocation method Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	reaction–diffusion models dynamical system involving the Lane–Emden-type equations spherical catalyst Lane–Emden problem spherical biocatalyst spectral collocation method Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 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
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.
format	article
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
title	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_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_sort	mathematical analysis of non-isothermal reaction–diffusion models arising in spherical catalyst and spherical biocatalyst
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/294d5a0f588442579a770807df7eccc9
work_keys_str_mv	AT vivekmanitripathi mathematicalanalysisofnonisothermalreactiondiffusionmodelsarisinginsphericalcatalystandsphericalbiocatalyst AT harimohansrivastava mathematicalanalysisofnonisothermalreactiondiffusionmodelsarisinginsphericalcatalystandsphericalbiocatalyst AT harendrasingh mathematicalanalysisofnonisothermalreactiondiffusionmodelsarisinginsphericalcatalystandsphericalbiocatalyst AT chetanswarup mathematicalanalysisofnonisothermalreactiondiffusionmodelsarisinginsphericalcatalystandsphericalbiocatalyst AT sudhanshuaggarwal mathematicalanalysisofnonisothermalreactiondiffusionmodelsarisinginsphericalcatalystandsphericalbiocatalyst
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Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst

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