Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation
Abstract In this article, the Taylor wavelet collocation method (TWCM) is presented for solving the nonlinear Rosenau–Hyman equation, which models nonlinear dispersion in liquid drop formation. TWCM outperforms existing methods, such as the Hermite wavelet and other semi-analytical approaches, by pr...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-04698-7 |
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| author | Mahmoud Abd El-Hady Mohamed El-Gamel Yasser Kashwaa |
| author_facet | Mahmoud Abd El-Hady Mohamed El-Gamel Yasser Kashwaa |
| author_sort | Mahmoud Abd El-Hady |
| collection | DOAJ |
| description | Abstract In this article, the Taylor wavelet collocation method (TWCM) is presented for solving the nonlinear Rosenau–Hyman equation, which models nonlinear dispersion in liquid drop formation. TWCM outperforms existing methods, such as the Hermite wavelet and other semi-analytical approaches, by providing higher computational efficiency and accuracy. The differential equation is converted into a system of algebraic equations, solved using the Broyden-Quasi Newton algorithm. Numerical examples demonstrate the reliability and robustness of TWCM in handling nonlinear dispersion patterns. All calculations and visualizations are performed using Matlab, showcasing the method’s effectiveness and advancement in analyzing nonlinear liquid dispersion. |
| format | Article |
| id | doaj-art-c7aeeb965fc643c59e85883216d81af0 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c7aeeb965fc643c59e85883216d81af02025-08-20T03:37:31ZengNature PortfolioScientific Reports2045-23222025-07-0115111710.1038/s41598-025-04698-7Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocationMahmoud Abd El-Hady0Mohamed El-Gamel1Yasser Kashwaa2Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura UniversityDepartment of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura UniversityDepartment of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura UniversityAbstract In this article, the Taylor wavelet collocation method (TWCM) is presented for solving the nonlinear Rosenau–Hyman equation, which models nonlinear dispersion in liquid drop formation. TWCM outperforms existing methods, such as the Hermite wavelet and other semi-analytical approaches, by providing higher computational efficiency and accuracy. The differential equation is converted into a system of algebraic equations, solved using the Broyden-Quasi Newton algorithm. Numerical examples demonstrate the reliability and robustness of TWCM in handling nonlinear dispersion patterns. All calculations and visualizations are performed using Matlab, showcasing the method’s effectiveness and advancement in analyzing nonlinear liquid dispersion.https://doi.org/10.1038/s41598-025-04698-7Taylor waveletCollocation methodRosenau–HymanOperational matrix |
| spellingShingle | Mahmoud Abd El-Hady Mohamed El-Gamel Yasser Kashwaa Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation Scientific Reports Taylor wavelet Collocation method Rosenau–Hyman Operational matrix |
| title | Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation |
| title_full | Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation |
| title_fullStr | Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation |
| title_full_unstemmed | Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation |
| title_short | Efficient numerical analysis of nonlinear liquid dispersion pattern drops using Taylor wavelet collocation |
| title_sort | efficient numerical analysis of nonlinear liquid dispersion pattern drops using taylor wavelet collocation |
| topic | Taylor wavelet Collocation method Rosenau–Hyman Operational matrix |
| url | https://doi.org/10.1038/s41598-025-04698-7 |
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