Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics
Abstract The present study uses the least squares residual power series (LSRPS) method to obtain approximate solutions to the nonlinear fractional-order Kawahara and Rosenau- Hyman equations. This method combines the residual power series (RPS) technique and the least squares approach. The calculati...
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Nature Portfolio
2025-04-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-97639-3 |
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| author | A. Hassan A. A. M. Arafa S. Z. Rida M. A. Dagher H. M. El Sherbiny |
| author_facet | A. Hassan A. A. M. Arafa S. Z. Rida M. A. Dagher H. M. El Sherbiny |
| author_sort | A. Hassan |
| collection | DOAJ |
| description | Abstract The present study uses the least squares residual power series (LSRPS) method to obtain approximate solutions to the nonlinear fractional-order Kawahara and Rosenau- Hyman equations. This method combines the residual power series (RPS) technique and the least squares approach. The calculations are obtained using Caputo’s sense as a basis. To obtain approximations of solutions, the well-known RPS method is first used. The functions are then proven to be linearly independent by checking the Wronskian determinant at fractional order. Next, a system of linear equations is generated and processed using the least squares approach. Using the least squares method, which uses fewer expansion terms than the classical RPS method, approximate solutions are determined. The problems presented below demonstrate how much faster the proposed method converges compared to the RPS method. Numerical results are presented to demonstrate the efficiency, accuracy, and rapid convergence of the method. |
| format | Article |
| id | doaj-art-0e6cd48a69a14cc7904f87f8a5b5f3e1 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-0e6cd48a69a14cc7904f87f8a5b5f3e12025-08-20T02:10:56ZengNature PortfolioScientific Reports2045-23222025-04-0115111710.1038/s41598-025-97639-3Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamicsA. Hassan0A. A. M. Arafa1S. Z. Rida2M. A. Dagher3H. M. El Sherbiny4Department of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez UniversityDepartment of Mathematics, College of Science, Qassim UniversityDepartment of Mathematics, Faculty of Science, South Valley UniversityDepartment of Science and Mathematical Engineering, Faculty of Petroleum and Mining Engineering, Suez UniversityDepartment of Mathematics and Computer Science, Faculty of Science, Suez UniversityAbstract The present study uses the least squares residual power series (LSRPS) method to obtain approximate solutions to the nonlinear fractional-order Kawahara and Rosenau- Hyman equations. This method combines the residual power series (RPS) technique and the least squares approach. The calculations are obtained using Caputo’s sense as a basis. To obtain approximations of solutions, the well-known RPS method is first used. The functions are then proven to be linearly independent by checking the Wronskian determinant at fractional order. Next, a system of linear equations is generated and processed using the least squares approach. Using the least squares method, which uses fewer expansion terms than the classical RPS method, approximate solutions are determined. The problems presented below demonstrate how much faster the proposed method converges compared to the RPS method. Numerical results are presented to demonstrate the efficiency, accuracy, and rapid convergence of the method.https://doi.org/10.1038/s41598-025-97639-3Fractional derivativesLeast squares approximationsResidual power series methodFractional WronskianKawahara equationRosenau-Hyman equation |
| spellingShingle | A. Hassan A. A. M. Arafa S. Z. Rida M. A. Dagher H. M. El Sherbiny Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics Scientific Reports Fractional derivatives Least squares approximations Residual power series method Fractional Wronskian Kawahara equation Rosenau-Hyman equation |
| title | Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics |
| title_full | Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics |
| title_fullStr | Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics |
| title_full_unstemmed | Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics |
| title_short | Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics |
| title_sort | least squares residual power series solutions for kawahara and rosenau hyman nonlinear wave interactions with applications in fluid dynamics |
| topic | Fractional derivatives Least squares approximations Residual power series method Fractional Wronskian Kawahara equation Rosenau-Hyman equation |
| url | https://doi.org/10.1038/s41598-025-97639-3 |
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