Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques
In this study, we investigate the traveling wave solutions of the Gilson-Pickering equation using two different approaches: F-expansion and (1/G$ ^\prime $)-expansion. To carry out the analysis, we perform a numerical study using the implicit finite difference approach on a uniform mesh and the para...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024595?viewType=HTML |
| _version_ | 1827288978397593600 |
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| author | Taghread Ghannam Alharbi Abdulghani Alharbi |
| author_facet | Taghread Ghannam Alharbi Abdulghani Alharbi |
| author_sort | Taghread Ghannam Alharbi |
| collection | DOAJ |
| description | In this study, we investigate the traveling wave solutions of the Gilson-Pickering equation using two different approaches: F-expansion and (1/G$ ^\prime $)-expansion. To carry out the analysis, we perform a numerical study using the implicit finite difference approach on a uniform mesh and the parabolic-Monge-Ampère (PMA) method on a moving mesh. We examine the truncation error, stability, and convergence of the difference scheme implemented on a fixed mesh. MATLAB software generates accurate representations of the solution based on specified parameter values by creating 3D and 2D graphs. Numerical simulations with the finite difference scheme demonstrate excellent agreement with the analytical solutions, further confirming the validity of our approaches. Convergence analysis confirms the stability and high accuracy of the implemented scheme. Notably, the PMA method performs better in capturing intricate wave interactions and dynamics that are not readily achievable with a fixed mesh. |
| first_indexed | 2024-04-24T11:40:49Z |
| format | Article |
| id | doaj.art-a4358564b2534c599128074b36fa0a65 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T11:40:49Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a4358564b2534c599128074b36fa0a652024-04-10T01:28:03ZengAIMS PressAIMS Mathematics2473-69882024-03-0195121881221010.3934/math.2024595Traveling-wave and numerical investigations to nonlinear equations via modern computational techniquesTaghread Ghannam Alharbi0Abdulghani Alharbi 1Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia; taghread1@hotmail.comDepartment of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia; taghread1@hotmail.comIn this study, we investigate the traveling wave solutions of the Gilson-Pickering equation using two different approaches: F-expansion and (1/G$ ^\prime $)-expansion. To carry out the analysis, we perform a numerical study using the implicit finite difference approach on a uniform mesh and the parabolic-Monge-Ampère (PMA) method on a moving mesh. We examine the truncation error, stability, and convergence of the difference scheme implemented on a fixed mesh. MATLAB software generates accurate representations of the solution based on specified parameter values by creating 3D and 2D graphs. Numerical simulations with the finite difference scheme demonstrate excellent agreement with the analytical solutions, further confirming the validity of our approaches. Convergence analysis confirms the stability and high accuracy of the implemented scheme. Notably, the PMA method performs better in capturing intricate wave interactions and dynamics that are not readily achievable with a fixed mesh.https://www.aimspress.com/article/doi/10.3934/math.2024595?viewType=HTMLgilson-pickering equationexact wave solutionsnumerical solutionsstabilityaccuracyparabolic-monge-ampere |
| spellingShingle | Taghread Ghannam Alharbi Abdulghani Alharbi Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques AIMS Mathematics gilson-pickering equation exact wave solutions numerical solutions stability accuracy parabolic-monge-ampere |
| title | Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques |
| title_full | Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques |
| title_fullStr | Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques |
| title_full_unstemmed | Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques |
| title_short | Traveling-wave and numerical investigations to nonlinear equations via modern computational techniques |
| title_sort | traveling wave and numerical investigations to nonlinear equations via modern computational techniques |
| topic | gilson-pickering equation exact wave solutions numerical solutions stability accuracy parabolic-monge-ampere |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024595?viewType=HTML |
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