An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method
In this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The ef...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024420?viewType=HTML |
| _version_ | 1797265599982731264 |
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| author | Shumoua F. Alrzqi Fatimah A. Alrawajeh Hany N. Hassan |
| author_facet | Shumoua F. Alrzqi Fatimah A. Alrawajeh Hany N. Hassan |
| author_sort | Shumoua F. Alrzqi |
| collection | DOAJ |
| description | In this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The efficiency, accuracy, and simplicity of the employed methodology were tested by solving eight different cases involving four examples of the single solitary wave with different parameter values, interactions between two solitary waves, interactions between three solitary waves, and evolution of solitons with Gaussian and undular bore initial conditions. The error norms were evaluated for the motion of the single solitary wave. The conservation properties of the GR–KDV–RLW equation were studied by computing the momentum and energy. Additionally, the numerical results were compared with the previous studies in the literature. |
| first_indexed | 2024-04-25T00:47:22Z |
| format | Article |
| id | doaj.art-5c8bddfadbf040088e0e83d286e499ca |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-25T00:47:22Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5c8bddfadbf040088e0e83d286e499ca2024-03-12T01:46:55ZengAIMS PressAIMS Mathematics2473-69882024-02-01948661868810.3934/math.2024420An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral methodShumoua F. Alrzqi0Fatimah A. Alrawajeh1Hany N. Hassan 21. Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia1. Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia2. Department of Basic Sciences, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi ArabiaIn this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The efficiency, accuracy, and simplicity of the employed methodology were tested by solving eight different cases involving four examples of the single solitary wave with different parameter values, interactions between two solitary waves, interactions between three solitary waves, and evolution of solitons with Gaussian and undular bore initial conditions. The error norms were evaluated for the motion of the single solitary wave. The conservation properties of the GR–KDV–RLW equation were studied by computing the momentum and energy. Additionally, the numerical results were compared with the previous studies in the literature.https://www.aimspress.com/article/doi/10.3934/math.2024420?viewType=HTMLgr–kdv–rlw equationfourier spectral methodfast fourier transformfinite differencesolitary waves |
| spellingShingle | Shumoua F. Alrzqi Fatimah A. Alrawajeh Hany N. Hassan An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method AIMS Mathematics gr–kdv–rlw equation fourier spectral method fast fourier transform finite difference solitary waves |
| title | An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method |
| title_full | An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method |
| title_fullStr | An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method |
| title_full_unstemmed | An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method |
| title_short | An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method |
| title_sort | efficient numerical technique for investigating the generalized rosenau kdv rlw equation by using the fourier spectral method |
| topic | gr–kdv–rlw equation fourier spectral method fast fourier transform finite difference solitary waves |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024420?viewType=HTML |
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