On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy
This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study p...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001111 |
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| author | Dilveen M. Ahmed Bewar A. Mahmood Ahmad Alalyani |
| author_facet | Dilveen M. Ahmed Bewar A. Mahmood Ahmad Alalyani |
| author_sort | Dilveen M. Ahmed |
| collection | DOAJ |
| description | This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields. |
| format | Article |
| id | doaj-art-1bb7344955cf4a789e5761271ee8749c |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-1bb7344955cf4a789e5761271ee8749c2025-08-20T03:53:17ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410118410.1016/j.padiff.2025.101184On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracyDilveen M. Ahmed0Bewar A. Mahmood1Ahmad Alalyani2Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Duhok, IraqDepartment of Mathematics, College of Science, University of Duhok, Kurdistan Region, Duhok, IraqDepartment of Mathematics, Faculty of Science, Al-Baha University, Al-Baha 65526, Saudi Arabia; Corresponding author.This paper addresses the numerical solution of the coupled Whitham–Broer–Kaup (WBK) problem, which has been widely investigated in engineering and physics. The WBK problem arises in various fields, including nonlinear optics, the theory of turbulence, fluid dynamics, and plasma physics. This study presents the variational homotopy perturbation method as a numerical technique for solving the coupled WBK problem. By merging the variational iteration method with the homotopy perturbation method, this approach provides accurate solutions without the need for linearization or discretization. The presented scheme is demonstrated by numerical examples that show it is easy to implement, offers superior outcomes compared to existing methods, and is both applicable and accurate. This paper introduces an improvement in numerical techniques for solving nonlinear partial differential equations, with important applications across various scientific and engineering fields.http://www.sciencedirect.com/science/article/pii/S2666818125001111Coupled Whitham–Broer–Kaup equationsVHPMNonlinear PDETraveling wave solutionVariational homotopy perturbation method |
| spellingShingle | Dilveen M. Ahmed Bewar A. Mahmood Ahmad Alalyani On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy Partial Differential Equations in Applied Mathematics Coupled Whitham–Broer–Kaup equations VHPM Nonlinear PDE Traveling wave solution Variational homotopy perturbation method |
| title | On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy |
| title_full | On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy |
| title_fullStr | On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy |
| title_full_unstemmed | On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy |
| title_short | On the solution of the coupled Whitham–Broer–Kaup problem using a hybrid technique for improved accuracy |
| title_sort | on the solution of the coupled whitham broer kaup problem using a hybrid technique for improved accuracy |
| topic | Coupled Whitham–Broer–Kaup equations VHPM Nonlinear PDE Traveling wave solution Variational homotopy perturbation method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001111 |
| work_keys_str_mv | AT dilveenmahmed onthesolutionofthecoupledwhithambroerkaupproblemusingahybridtechniqueforimprovedaccuracy AT bewaramahmood onthesolutionofthecoupledwhithambroerkaupproblemusingahybridtechniqueforimprovedaccuracy AT ahmadalalyani onthesolutionofthecoupledwhithambroerkaupproblemusingahybridtechniqueforimprovedaccuracy |