Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study
Abstract The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. Th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-01-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-52059-7 |
| _version_ | 1797349983409668096 |
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| author | Safia Malik Syeda Tehmina Ejaz Ali Akgül Murad Khan Hassani |
| author_facet | Safia Malik Syeda Tehmina Ejaz Ali Akgül Murad Khan Hassani |
| author_sort | Safia Malik |
| collection | DOAJ |
| description | Abstract The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures. Additionally, a comparative analysis is conducted between the numerical outcomes of the proposed technique with previously published methods to validate the correctness and accuracy of the current approach. The primary objective of this research is to investigate the application of subdivision schemes in the fields of physical sciences and engineering. Our approach involves transforming the problem into a set of algebraic equations. |
| first_indexed | 2024-03-08T12:38:13Z |
| format | Article |
| id | doaj.art-3449caeb0f8e4196ad3a6d40f6f47c23 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-08T12:38:13Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-3449caeb0f8e4196ad3a6d40f6f47c232024-01-21T12:17:39ZengNature PortfolioScientific Reports2045-23222024-01-0114111810.1038/s41598-024-52059-7Exploring the advection-diffusion equation through the subdivision collocation method: a numerical studySafia Malik0Syeda Tehmina Ejaz1Ali Akgül2Murad Khan Hassani3Department of Mathematics, The Government Sadiq College Women University BahawalpurDepartment of Mathematics, The Government Sadiq College Women University BahawalpurDepartment of Computer Science and Mathematics, Lebanese American UniversityDepartment of Mathematics, Ghazni UniversityAbstract The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures. Additionally, a comparative analysis is conducted between the numerical outcomes of the proposed technique with previously published methods to validate the correctness and accuracy of the current approach. The primary objective of this research is to investigate the application of subdivision schemes in the fields of physical sciences and engineering. Our approach involves transforming the problem into a set of algebraic equations.https://doi.org/10.1038/s41598-024-52059-7 |
| spellingShingle | Safia Malik Syeda Tehmina Ejaz Ali Akgül Murad Khan Hassani Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study Scientific Reports |
| title | Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study |
| title_full | Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study |
| title_fullStr | Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study |
| title_full_unstemmed | Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study |
| title_short | Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study |
| title_sort | exploring the advection diffusion equation through the subdivision collocation method a numerical study |
| url | https://doi.org/10.1038/s41598-024-52059-7 |
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