Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves
This article investigates fluid flow in a dynamic system using the coupled Boussinesq–Burgers equation to precisely narrate the propagation of shallow water waves. This work proposes a novel approach to using the quintic B-spline technique to obtain an approximate solution to the nonlinear fractiona...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-08-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2025-0191 |
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| author | Wang Xiaoming Ghafoor Usama Abbas Muhammad Abdullah Farah Aini Hamed Yasser Salah |
| author_facet | Wang Xiaoming Ghafoor Usama Abbas Muhammad Abdullah Farah Aini Hamed Yasser Salah |
| author_sort | Wang Xiaoming |
| collection | DOAJ |
| description | This article investigates fluid flow in a dynamic system using the coupled Boussinesq–Burgers equation to precisely narrate the propagation of shallow water waves. This work proposes a novel approach to using the quintic B-spline technique to obtain an approximate solution to the nonlinear fractional coupled Boussinesq–Burgers equation. For discretizing time, the Caputo fractional derivative is used to handle the fractional derivative effectively, while the quintic B-spline function is used to interpolate the spatial derivative. We provide two numerical examples to show the level of accuracy and practicality of the current scheme in solving the fractional coupled Boussinesq–Burgers problem and see how observe the effect of the fractional-order on wave propagation. In addition, we conduct a stability analyzis and numerically determine the order of convergence. We compute the error norms to assess the accuracy of the proposed method. |
| format | Article |
| id | doaj-art-be914a76314a4c9bbe7ed4863b832a53 |
| institution | Kabale University |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-be914a76314a4c9bbe7ed4863b832a532025-08-20T03:46:52ZengDe GruyterOpen Physics2391-54712025-08-012312314810.1515/phys-2025-0191Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water wavesWang Xiaoming0Ghafoor Usama1Abbas Muhammad2Abdullah Farah Aini3Hamed Yasser Salah4School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, ChinaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau Pinang, MalaysiaDepartment of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaThis article investigates fluid flow in a dynamic system using the coupled Boussinesq–Burgers equation to precisely narrate the propagation of shallow water waves. This work proposes a novel approach to using the quintic B-spline technique to obtain an approximate solution to the nonlinear fractional coupled Boussinesq–Burgers equation. For discretizing time, the Caputo fractional derivative is used to handle the fractional derivative effectively, while the quintic B-spline function is used to interpolate the spatial derivative. We provide two numerical examples to show the level of accuracy and practicality of the current scheme in solving the fractional coupled Boussinesq–Burgers problem and see how observe the effect of the fractional-order on wave propagation. In addition, we conduct a stability analyzis and numerically determine the order of convergence. We compute the error norms to assess the accuracy of the proposed method.https://doi.org/10.1515/phys-2025-0191boussinesq–burgers equationquintic b-spline functionscaputo time fractional derivativefinite difference techniquestability |
| spellingShingle | Wang Xiaoming Ghafoor Usama Abbas Muhammad Abdullah Farah Aini Hamed Yasser Salah Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves Open Physics boussinesq–burgers equation quintic b-spline functions caputo time fractional derivative finite difference technique stability |
| title | Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves |
| title_full | Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves |
| title_fullStr | Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves |
| title_full_unstemmed | Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves |
| title_short | Effectual quintic B-spline functions for solving the time fractional coupled Boussinesq–Burgers equation arising in shallow water waves |
| title_sort | effectual quintic b spline functions for solving the time fractional coupled boussinesq burgers equation arising in shallow water waves |
| topic | boussinesq–burgers equation quintic b-spline functions caputo time fractional derivative finite difference technique stability |
| url | https://doi.org/10.1515/phys-2025-0191 |
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