Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers
In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term is studied. The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered...
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| Veröffentlicht in: | Indian journal of pure and applied mathematics 2023-09, Vol.54 (3), p.675-688 |
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| container_title | Indian journal of pure and applied mathematics |
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| creator | Chawla, Sheetal Urmil Singh, Jagbir |
| description | In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term is studied. The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered system does not obey maximum principle. Forward-backward approximation is used for the Robin boundary conditions and a central finite difference approximation is proposed for the differential system in conjunction with piecewise uniform Shishkin meshes and graded Bakhvalov meshes. The scheme is proved to be an almost first-order parameter uniform convergent. Numerical experiments are presented which are in line with the theoretical findings. |
| doi_str_mv | 10.1007/s13226-022-00285-y |
| format | Article |
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The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered system does not obey maximum principle. Forward-backward approximation is used for the Robin boundary conditions and a central finite difference approximation is proposed for the differential system in conjunction with piecewise uniform Shishkin meshes and graded Bakhvalov meshes. The scheme is proved to be an almost first-order parameter uniform convergent. Numerical experiments are presented which are in line with the theoretical findings.</description><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Boundary conditions</subject><subject>Boundary value problems</subject><subject>Diffusion layers</subject><subject>Finite difference method</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maximum principle</subject><subject>Numerical Analysis</subject><subject>Numerical methods</subject><subject>Order parameters</subject><subject>Original Research</subject><subject>Perturbation</subject><subject>Reaction-diffusion equations</subject><issn>0019-5588</issn><issn>0975-7465</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UctKAzEUHUTBWv0BVwHX0Twmj1lKsSoU3Og6ZGaSdso0qXkU5mP8V6MVunN1z733nMOBU1W3GN1jhMRDxJQQDhEhECEiGZzOqhlqBIOi5uy8YIQbyJiUl9VVjFuEOEVNM6u-lkNKpgc7EzfA5Z0JQ6fHsqaN74H1AWjQ-bwfCydOMZkd8BbEwa3zqMM4gb0JKYe2vIPRXRq8g_1gbY4FgeDbwYHWZ9frMIGDHrMB-3Idi89GH4rN6atdDwaXTHAlwKgnE-J1dWH1GM3N35xXH8un98ULXL09vy4eV7AjAiVIWia41ZRLgq3AtOWmq20vmJWUcSIopxwTZGurCe60bbHghhrZUk40kT2dV3dH35LtM5uY1NbnnxxREVnLmjIqm8IiR1YXfIzBWLUPw65EVxipnxrUsQZValC_NaipiOhRFAvZrU04Wf-j-gYmA498</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Chawla, Sheetal</creator><creator>Urmil</creator><creator>Singh, Jagbir</creator><general>Indian National Science Academy</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230901</creationdate><title>Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers</title><author>Chawla, Sheetal ; Urmil ; Singh, Jagbir</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-2b576fa36821f713b6ec4fd75f8356273636120f4fa21cafb176e3e8b362a28d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Boundary conditions</topic><topic>Boundary value problems</topic><topic>Diffusion layers</topic><topic>Finite difference method</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Maximum principle</topic><topic>Numerical Analysis</topic><topic>Numerical methods</topic><topic>Order parameters</topic><topic>Original Research</topic><topic>Perturbation</topic><topic>Reaction-diffusion equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chawla, Sheetal</creatorcontrib><creatorcontrib>Urmil</creatorcontrib><creatorcontrib>Singh, Jagbir</creatorcontrib><collection>CrossRef</collection><jtitle>Indian journal of pure and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chawla, Sheetal</au><au>Urmil</au><au>Singh, Jagbir</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers</atitle><jtitle>Indian journal of pure and applied mathematics</jtitle><stitle>Indian J Pure Appl Math</stitle><date>2023-09-01</date><risdate>2023</risdate><volume>54</volume><issue>3</issue><spage>675</spage><epage>688</epage><pages>675-688</pages><issn>0019-5588</issn><eissn>0975-7465</eissn><abstract>In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term is studied. The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered system does not obey maximum principle. Forward-backward approximation is used for the Robin boundary conditions and a central finite difference approximation is proposed for the differential system in conjunction with piecewise uniform Shishkin meshes and graded Bakhvalov meshes. The scheme is proved to be an almost first-order parameter uniform convergent. Numerical experiments are presented which are in line with the theoretical findings.</abstract><cop>New Delhi</cop><pub>Indian National Science Academy</pub><doi>10.1007/s13226-022-00285-y</doi><tpages>14</tpages></addata></record> |
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| subjects | Applications of Mathematics Approximation Boundary conditions Boundary value problems Diffusion layers Finite difference method Mathematics Mathematics and Statistics Maximum principle Numerical Analysis Numerical methods Order parameters Original Research Perturbation Reaction-diffusion equations |
| title | Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers |
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