Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations
This paper presents a robust fitted mesh finite difference method for solving a system of <i>n</i> singularly perturbed two parameter convection–reaction–diffusion delay differential equations defined on the interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/...
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MDPI AG
2025-03-01
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| author | Joseph Paramasivam Mathiyazhagan Jenolin Arthur George E. Chatzarakis S. L. Panetsos |
| author_facet | Joseph Paramasivam Mathiyazhagan Jenolin Arthur George E. Chatzarakis S. L. Panetsos |
| author_sort | Joseph Paramasivam Mathiyazhagan |
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| description | This paper presents a robust fitted mesh finite difference method for solving a system of <i>n</i> singularly perturbed two parameter convection–reaction–diffusion delay differential equations defined on the interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>. Leveraging a piecewise uniform Shishkin mesh, the method adeptly captures the solution’s behavior arising from delay term and small perturbation parameters. The proposed numerical scheme is rigorously analyzed and proven to be parameter-robust, exhibiting nearly first-order convergence. A numerical illustration is included to validate the method’s efficiency and to confirm the theoretical predictions. |
| format | Article |
| id | doaj-art-87cab21678c64610b4e58d2604f67b98 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-87cab21678c64610b4e58d2604f67b982025-08-20T03:14:20ZengMDPI AGAxioms2075-16802025-03-0114424610.3390/axioms14040246Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential EquationsJoseph Paramasivam Mathiyazhagan0Jenolin Arthur1George E. Chatzarakis2S. L. Panetsos3PG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Tiruchirappalli 620 017, Tamil Nadu, IndiaPG & Research Department of Mathematics, Bishop Heber College (Affiliated to Bharathidasan University), Tiruchirappalli 620 017, Tamil Nadu, IndiaDepartment of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, GreeceDepartment of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), 15122 Marousi, GreeceThis paper presents a robust fitted mesh finite difference method for solving a system of <i>n</i> singularly perturbed two parameter convection–reaction–diffusion delay differential equations defined on the interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>. Leveraging a piecewise uniform Shishkin mesh, the method adeptly captures the solution’s behavior arising from delay term and small perturbation parameters. The proposed numerical scheme is rigorously analyzed and proven to be parameter-robust, exhibiting nearly first-order convergence. A numerical illustration is included to validate the method’s efficiency and to confirm the theoretical predictions.https://www.mdpi.com/2075-1680/14/4/246singularly perturbed delay differential equationsnumerical methodsconvection–diffusion equationsShishkin meshesboundary layeruniform convergence |
| spellingShingle | Joseph Paramasivam Mathiyazhagan Jenolin Arthur George E. Chatzarakis S. L. Panetsos Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations Axioms singularly perturbed delay differential equations numerical methods convection–diffusion equations Shishkin meshes boundary layer uniform convergence |
| title | Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations |
| title_full | Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations |
| title_fullStr | Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations |
| title_full_unstemmed | Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations |
| title_short | Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations |
| title_sort | efficient layer resolving fitted mesh finite difference approach for solving a system of n two parameter singularly perturbed convection diffusion delay differential equations |
| topic | singularly perturbed delay differential equations numerical methods convection–diffusion equations Shishkin meshes boundary layer uniform convergence |
| url | https://www.mdpi.com/2075-1680/14/4/246 |
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