Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations
In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to f...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6636607 |
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| author | P. Hammachukiattikul E. Sekar A. Tamilselvan R. Vadivel N. Gunasekaran Praveen Agarwal |
| author_facet | P. Hammachukiattikul E. Sekar A. Tamilselvan R. Vadivel N. Gunasekaran Praveen Agarwal |
| author_sort | P. Hammachukiattikul |
| collection | DOAJ |
| description | In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20). |
| format | Article |
| id | doaj-art-922128226a3b4af3a020f7369ad20399 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-922128226a3b4af3a020f7369ad203992025-02-03T07:24:01ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66366076636607Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential EquationsP. Hammachukiattikul0E. Sekar1A. Tamilselvan2R. Vadivel3N. Gunasekaran4Praveen Agarwal5Department of Mathematics, Phuket Rajabhat University, 83000 Phuket, ThailandDepartment of Mathematics, SASTRA Deemed to be University, Thanjavur, Tamilnadu 613401, IndiaDepartment of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, IndiaDepartment of Mathematics, Phuket Rajabhat University, 83000 Phuket, ThailandDepartment of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, JapanDepartment of Mathematics, Anand International College of Engineering, Jaipur, IndiaIn this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20).http://dx.doi.org/10.1155/2021/6636607 |
| spellingShingle | P. Hammachukiattikul E. Sekar A. Tamilselvan R. Vadivel N. Gunasekaran Praveen Agarwal Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations Journal of Mathematics |
| title | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| title_full | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| title_fullStr | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| title_full_unstemmed | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| title_short | Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations |
| title_sort | comparative study on numerical methods for singularly perturbed advanced delay differential equations |
| url | http://dx.doi.org/10.1155/2021/6636607 |
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