Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay
The mathematical model pertaining to the cubic-autocatalytic reaction with M-M decay considered in one- dimensional reaction-diffusion cell is discussed. Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady...
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| creator | Ananthaswamy, V. Narmatha, S. |
| description | The mathematical model pertaining to the cubic-autocatalytic reaction with M-M decay considered in one- dimensional reaction-diffusion cell is discussed. Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters. |
| doi_str_mv | 10.1063/5.0058275 |
| format | Conference Proceeding |
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Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/5.0058275</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Decay ; Diffusion cells ; Exact solutions ; Mathematical models ; Reaction-diffusion equations ; Steady state</subject><ispartof>AIP conference proceedings, 2021, Vol.2378 (1)</ispartof><rights>Author(s)</rights><rights>2021 Author(s). 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Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters.</description><subject>Decay</subject><subject>Diffusion cells</subject><subject>Exact solutions</subject><subject>Mathematical models</subject><subject>Reaction-diffusion equations</subject><subject>Steady state</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2021</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNo9kE9LwzAYxoMoOKcHv0HAm5CZpEmTHMfwH2x4UfBW0jRhGTXtmhTdzbNXv6GfxNYNTy88_N4Hfg8AlwTPCM6zGz7DmEsq-BGYEM4JEjnJj8EEY8UQZdnrKTiLcYMxVULICfiat23XfPg3nSzUQde75I2uYWzqPvkmwMbB0ARU-2B1BzurzRijyjvXxxGw216PUYQ-QA1NX3qDdJ8ao9O-7v8Lvvu0hitv1trWPv58fq9sSDbAyhq9OwcnTtfRXhzuFLzc3T4vHtDy6f5xMV-ilmRZQkpSw5njmChFnRIKO2koE1VpOWaVIdyUhLkSO6FKo6SRmZGCO84EkaRi2RRc7XsH8W1vYyo2Td8N6rGgA5QLktORut5T0fj0J1i03TBTtysILsatC14cts5-Ac3UdKo</recordid><startdate>20210702</startdate><enddate>20210702</enddate><creator>Ananthaswamy, V.</creator><creator>Narmatha, S.</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20210702</creationdate><title>Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay</title><author>Ananthaswamy, V. ; Narmatha, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p133t-982c54f501992f9790f8c247dbe504dc15cb14fb0f79bc98c83c875f547181d43</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Decay</topic><topic>Diffusion cells</topic><topic>Exact solutions</topic><topic>Mathematical models</topic><topic>Reaction-diffusion equations</topic><topic>Steady state</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ananthaswamy, V.</creatorcontrib><creatorcontrib>Narmatha, S.</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ananthaswamy, V.</au><au>Narmatha, S.</au><au>Vijayan, V.</au><au>Dinesh, S.</au><au>Srinivasan, R.</au><au>Parthiban, A.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay</atitle><btitle>AIP conference proceedings</btitle><date>2021-07-02</date><risdate>2021</risdate><volume>2378</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>The mathematical model pertaining to the cubic-autocatalytic reaction with M-M decay considered in one- dimensional reaction-diffusion cell is discussed. Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0058275</doi><tpages>24</tpages></addata></record> |
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| source | American Institute of Physics |
| subjects | Decay Diffusion cells Exact solutions Mathematical models Reaction-diffusion equations Steady state |
| title | Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay |
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