Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension
This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and...
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/1980 |
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| author | Akeel A. AL-saedi Omid Nikan Zakieh Avazzadeh António M. Lopes |
| author_facet | Akeel A. AL-saedi Omid Nikan Zakieh Avazzadeh António M. Lopes |
| author_sort | Akeel A. AL-saedi |
| collection | DOAJ |
| description | This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation. |
| first_indexed | 2024-03-09T16:25:16Z |
| format | Article |
| id | doaj.art-1ca442b28cca4a1788cbb395b9166793 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:25:16Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1ca442b28cca4a1788cbb395b91667932023-11-24T15:08:37ZengMDPI AGSymmetry2073-89942023-10-011511198010.3390/sym15111980Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface TensionAkeel A. AL-saedi0Omid Nikan1Zakieh Avazzadeh2António M. Lopes3Department of Mathematics, College of Education, Misan University, Misan 62001, IraqSchool of Mathematics and Computer Science, Iran University of Science and Technology, Tehran 16846-13114, IranDepartment of Mathematical Sciences, University of South Africa, Florida 0003, South AfricaLAETA/INEG, Faculty of Engineering, University of Porto, 4200-465 Porto, PortugalThis paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.https://www.mdpi.com/2073-8994/15/11/1980generalized Rosenau–Kawahara–RLWsolitary wave solutionslocal meshless technique |
| spellingShingle | Akeel A. AL-saedi Omid Nikan Zakieh Avazzadeh António M. Lopes Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension Symmetry generalized Rosenau–Kawahara–RLW solitary wave solutions local meshless technique |
| title | Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension |
| title_full | Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension |
| title_fullStr | Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension |
| title_full_unstemmed | Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension |
| title_short | Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension |
| title_sort | solitary wave propagation of the generalized rosenau kawahara rlw equation in shallow water theory with surface tension |
| topic | generalized Rosenau–Kawahara–RLW solitary wave solutions local meshless technique |
| url | https://www.mdpi.com/2073-8994/15/11/1980 |
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