Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations
The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations. Meanwhile, homotopy perturbation method yields...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | Indonesian |
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Universitas Islam Negeri Raden Intan Lampung
2021-07-01
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| Series: | Desimal |
| Subjects: | |
| Online Access: | http://ejournal.radenintan.ac.id/index.php/desimal/article/view/7825 |
| _version_ | 1798026779651211264 |
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| author | Atika Faradilla Aang Nuryaman Asmiati Asmiati Dewi Rakhmatia Nur |
| author_facet | Atika Faradilla Aang Nuryaman Asmiati Asmiati Dewi Rakhmatia Nur |
| author_sort | Atika Faradilla |
| collection | DOAJ |
| description | The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations. Meanwhile, homotopy perturbation method yields a very rapid convergence of the solution series in most cases. The developed method, variational homotopy perturbation method, took full advantage of both methods. In this study, we described an application of the variational homotopy perturbation method to solve systems of homogeneous partial differential equations. Here we consider some initial value problems of homogeneous partial differential equation systems with two and three variables. The results show that the obtained solution using this method was in agreement with the solution using the homotopy analysis method and variational iteration method, which prove the validity of the variational homotopy perturbation method when applied to systems of partial differential equations. |
| first_indexed | 2024-04-11T18:40:49Z |
| format | Article |
| id | doaj.art-8c50949b48d14a5dbbbddab3f1cc92f9 |
| institution | Directory Open Access Journal |
| issn | 2613-9073 2613-9081 |
| language | Indonesian |
| last_indexed | 2024-04-11T18:40:49Z |
| publishDate | 2021-07-01 |
| publisher | Universitas Islam Negeri Raden Intan Lampung |
| record_format | Article |
| series | Desimal |
| spelling | doaj.art-8c50949b48d14a5dbbbddab3f1cc92f92022-12-22T04:08:58ZindUniversitas Islam Negeri Raden Intan LampungDesimal2613-90732613-90812021-07-014213314410.24042/djm.v4i2.78253962Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equationsAtika Faradilla0Aang Nuryaman1Asmiati Asmiati2Dewi Rakhmatia Nur3Universitas LampungUniversitas LampungUniversitas LampungUniversitas LampungThe variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations. Meanwhile, homotopy perturbation method yields a very rapid convergence of the solution series in most cases. The developed method, variational homotopy perturbation method, took full advantage of both methods. In this study, we described an application of the variational homotopy perturbation method to solve systems of homogeneous partial differential equations. Here we consider some initial value problems of homogeneous partial differential equation systems with two and three variables. The results show that the obtained solution using this method was in agreement with the solution using the homotopy analysis method and variational iteration method, which prove the validity of the variational homotopy perturbation method when applied to systems of partial differential equations.http://ejournal.radenintan.ac.id/index.php/desimal/article/view/7825variational homotopy perturbation methodvariational iteration methodhomotopy perturbation methodpartial differential equation system. |
| spellingShingle | Atika Faradilla Aang Nuryaman Asmiati Asmiati Dewi Rakhmatia Nur Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations Desimal variational homotopy perturbation method variational iteration method homotopy perturbation method partial differential equation system. |
| title | Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| title_full | Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| title_fullStr | Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| title_full_unstemmed | Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| title_short | Variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| title_sort | variational homotopy perturbation method for solving systems of homogeneous linear and nonlinear partial differential equations |
| topic | variational homotopy perturbation method variational iteration method homotopy perturbation method partial differential equation system. |
| url | http://ejournal.radenintan.ac.id/index.php/desimal/article/view/7825 |
| work_keys_str_mv | AT atikafaradilla variationalhomotopyperturbationmethodforsolvingsystemsofhomogeneouslinearandnonlinearpartialdifferentialequations AT aangnuryaman variationalhomotopyperturbationmethodforsolvingsystemsofhomogeneouslinearandnonlinearpartialdifferentialequations AT asmiatiasmiati variationalhomotopyperturbationmethodforsolvingsystemsofhomogeneouslinearandnonlinearpartialdifferentialequations AT dewirakhmatianur variationalhomotopyperturbationmethodforsolvingsystemsofhomogeneouslinearandnonlinearpartialdifferentialequations |