ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD
In this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method. Homotopy was built with embedding parameter p∈[0,1] which undergo...
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Universitas Pattimura
2023-06-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/6597 |
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| author | Mashuri Mashuri Yayah Zakiyah Rina Reorita |
| author_facet | Mashuri Mashuri Yayah Zakiyah Rina Reorita |
| author_sort | Mashuri Mashuri |
| collection | DOAJ |
| description | In this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method. Homotopy was built with embedding parameter p∈[0,1] which undergoes a deformation process from linear problems to nonlinear problems and the assumed solution of the KdV equation is expressed in the form of a power series p up to the third order. The result show that in each order solution we obtained resonance term. for handling the condition, we used Lindsteadt-Poincare method.the wave number k2 and dispersion relation can be obtained in the second order solution as the effect of using Lindsteadt-Poincare method. |
| format | Article |
| id | doaj-art-e03bc74f056b44e2b0af09a148f9f300 |
| institution | DOAJ |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-e03bc74f056b44e2b0af09a148f9f3002025-08-20T03:05:41ZengUniversitas PattimuraBarekeng1978-72272615-30172023-06-011720609061410.30598/barekengvol17iss2pp0609-06146597ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHODMashuri Mashuri0Yayah Zakiyah1Rina Reorita2Department of Mathematics, FMIPA, Universitas Jenderal Soedirman, IndonesiaDepartment of Mathematics, FMIPA, Universitas Jenderal Soedirman, IndonesiaDepartment of Mathematics, FMIPA, Universitas Jenderal Soedirman, IndonesiaIn this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method. Homotopy was built with embedding parameter p∈[0,1] which undergoes a deformation process from linear problems to nonlinear problems and the assumed solution of the KdV equation is expressed in the form of a power series p up to the third order. The result show that in each order solution we obtained resonance term. for handling the condition, we used Lindsteadt-Poincare method.the wave number k2 and dispersion relation can be obtained in the second order solution as the effect of using Lindsteadt-Poincare method.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/6597kdv equationhomotopyperturbation methodlindsteadt-poincare method |
| spellingShingle | Mashuri Mashuri Yayah Zakiyah Rina Reorita ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD Barekeng kdv equation homotopy perturbation method lindsteadt-poincare method |
| title | ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD |
| title_full | ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD |
| title_fullStr | ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD |
| title_full_unstemmed | ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD |
| title_short | ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD |
| title_sort | on the third order solution of kdv equation by using homotopy perturbation method |
| topic | kdv equation homotopy perturbation method lindsteadt-poincare method |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/6597 |
| work_keys_str_mv | AT mashurimashuri onthethirdordersolutionofkdvequationbyusinghomotopyperturbationmethod AT yayahzakiyah onthethirdordersolutionofkdvequationbyusinghomotopyperturbationmethod AT rinareorita onthethirdordersolutionofkdvequationbyusinghomotopyperturbationmethod |