Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate
Abstract This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. The innovation of this approach stems from its unique integration of three key elements:...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02000-2 |
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| _version_ | 1823861719900880896 |
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| author | Dany Joy Dinesh Kumar S Fathalla A Rihan |
| author_facet | Dany Joy Dinesh Kumar S Fathalla A Rihan |
| author_sort | Dany Joy |
| collection | DOAJ |
| description | Abstract This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. The innovation of this approach stems from its unique integration of three key elements: the Numerov method, known for its accuracy in solving second-order ODEs; a fitting factor, which improves handling of the singular perturbation parameter essential for accurately modeling SPDDEs; and the Taylor series expansion, which approximates first-order derivative terms, facilitating the application of the Numerov method to the system. Numerical experiments are conducted with varying perturbation parameters and mesh sizes to validate the method’s effectiveness. The results, expressed in terms of maximum absolute errors and the rate of convergence, demonstrate that the proposed approach achieves first-order uniform convergence. |
| format | Article |
| id | doaj-art-558a09994d13434a8a36ac1700502096 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-558a09994d13434a8a36ac17005020962025-02-09T12:47:44ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025112210.1186/s13661-025-02000-2Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rateDany Joy0Dinesh Kumar S1Fathalla A Rihan2Department of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematical Sciences, College of Science, UAE UniversityAbstract This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. The innovation of this approach stems from its unique integration of three key elements: the Numerov method, known for its accuracy in solving second-order ODEs; a fitting factor, which improves handling of the singular perturbation parameter essential for accurately modeling SPDDEs; and the Taylor series expansion, which approximates first-order derivative terms, facilitating the application of the Numerov method to the system. Numerical experiments are conducted with varying perturbation parameters and mesh sizes to validate the method’s effectiveness. The results, expressed in terms of maximum absolute errors and the rate of convergence, demonstrate that the proposed approach achieves first-order uniform convergence.https://doi.org/10.1186/s13661-025-02000-2Singular perturbationLarge delayWeakly coupled systemNumerical approximationError analysis |
| spellingShingle | Dany Joy Dinesh Kumar S Fathalla A Rihan Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate Boundary Value Problems Singular perturbation Large delay Weakly coupled system Numerical approximation Error analysis |
| title | Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| title_full | Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| title_fullStr | Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| title_full_unstemmed | Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| title_short | Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| title_sort | advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate |
| topic | Singular perturbation Large delay Weakly coupled system Numerical approximation Error analysis |
| url | https://doi.org/10.1186/s13661-025-02000-2 |
| work_keys_str_mv | AT danyjoy advancingnumericalsolutionsforasystemofsingularlyperturbeddelaydifferentialequationsatlinearrate AT dineshkumars advancingnumericalsolutionsforasystemofsingularlyperturbeddelaydifferentialequationsatlinearrate AT fathallaarihan advancingnumericalsolutionsforasystemofsingularlyperturbeddelaydifferentialequationsatlinearrate |