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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Main Authors: Mahmoud Abd El-Hady, Mohamed El-Gamel, Yasser Kashwaa
Format: Article
Language:English
Published: Nature Portfolio 2025-07-01
Series:Scientific Reports
Subjects:
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
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institution Kabale University
issn 2045-2322
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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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AT mohamedelgamel efficientnumericalanalysisofnonlinearliquiddispersionpatterndropsusingtaylorwaveletcollocation
AT yasserkashwaa efficientnumericalanalysisofnonlinearliquiddispersionpatterndropsusingtaylorwaveletcollocation