Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems
In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2021-01-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/12057 |
| _version_ | 1818656157446701056 |
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| author | Saeid Abbasbandy Hussein Sahihi Tofigh Allahviranloo |
| author_facet | Saeid Abbasbandy Hussein Sahihi Tofigh Allahviranloo |
| author_sort | Saeid Abbasbandy |
| collection | DOAJ |
| description | In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved. |
| first_indexed | 2024-12-17T03:21:07Z |
| format | Article |
| id | doaj.art-8cfe563cf79a4c4f8ebcb28199882efa |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-17T03:21:07Z |
| publishDate | 2021-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-8cfe563cf79a4c4f8ebcb28199882efa2022-12-21T22:05:31ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102021-01-0126111613410.3846/mma.2021.1205712057Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problemsSaeid Abbasbandy0Hussein Sahihi1Tofigh Allahviranloo2Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, 34149-16818 Qazvin, IranDepartment of Mathematics, Science and Research Branch, Islamic Azad University, 14778 Tehran, IranFaculty of Engineering and Natural Sciences, Bahcesehir University, 34353 Istanbul, TurkeyIn the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.https://journals.vgtu.lt/index.php/MMA/article/view/12057reproducing kernel methodsingularly perturbed parabolic problemserror analysisboundary layer behavior |
| spellingShingle | Saeid Abbasbandy Hussein Sahihi Tofigh Allahviranloo Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems Mathematical Modelling and Analysis reproducing kernel method singularly perturbed parabolic problems error analysis boundary layer behavior |
| title | Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems |
| title_full | Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems |
| title_fullStr | Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems |
| title_full_unstemmed | Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems |
| title_short | Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems |
| title_sort | implementing reproducing kernel method to solve singularly perturbed convection diffusion parabolic problems |
| topic | reproducing kernel method singularly perturbed parabolic problems error analysis boundary layer behavior |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/12057 |
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