Approximate solution to a generalized Van der Pol equation arising in plasma oscillations
Motivated by some published theoretical investigations and based on the two-fluid model, nonlinear plasma oscillations are analyzed and discussed in the framework of the generalized Van der Pol equation. This equation is analyzed and solved using two different analytical approaches. In this first ap...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2022-10-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0103138 |
| _version_ | 1828335596147310592 |
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| author | Weaam Alhejaili Alvaro H. Salas S. A. El-Tantawy |
| author_facet | Weaam Alhejaili Alvaro H. Salas S. A. El-Tantawy |
| author_sort | Weaam Alhejaili |
| collection | DOAJ |
| description | Motivated by some published theoretical investigations and based on the two-fluid model, nonlinear plasma oscillations are analyzed and discussed in the framework of the generalized Van der Pol equation. This equation is analyzed and solved using two different analytical approaches. In this first approach, the ansatz method is carried out for deriving an approximation in the form of a trigonometric function. In the second approach, the Krylov–Bogoliubov–Mitropolsky (KBM) technique is applied for obtaining a high-accurate approximation. The obtained approximations are compared with the numerical approximation using the Runge–Kutta (RK) method. Moreover, the distance error between the obtained approximations (using the ansatz method and the KBM technique) and the RK numerical approximation is estimated. In our investigation, both the proposed methods and obtained approximations can help many authors investigate several nonlinear oscillations in different plasma models and fluid mechanics. |
| first_indexed | 2024-04-13T21:49:29Z |
| format | Article |
| id | doaj.art-e47d6f40caa4465aa39bcc7cddbab1d8 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-04-13T21:49:29Z |
| publishDate | 2022-10-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-e47d6f40caa4465aa39bcc7cddbab1d82022-12-22T02:28:28ZengAIP Publishing LLCAIP Advances2158-32262022-10-011210105104105104-910.1063/5.0103138Approximate solution to a generalized Van der Pol equation arising in plasma oscillationsWeaam Alhejaili0Alvaro H. Salas1S. A. El-Tantawy2Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics and Statistics, Universidad Nacional de Colombia, FIZMAKO Research Group, Bogotá 111321, ColombiaDepartment of Physics, Faculty of Science, Port Said University, Port Said 42521, EgyptMotivated by some published theoretical investigations and based on the two-fluid model, nonlinear plasma oscillations are analyzed and discussed in the framework of the generalized Van der Pol equation. This equation is analyzed and solved using two different analytical approaches. In this first approach, the ansatz method is carried out for deriving an approximation in the form of a trigonometric function. In the second approach, the Krylov–Bogoliubov–Mitropolsky (KBM) technique is applied for obtaining a high-accurate approximation. The obtained approximations are compared with the numerical approximation using the Runge–Kutta (RK) method. Moreover, the distance error between the obtained approximations (using the ansatz method and the KBM technique) and the RK numerical approximation is estimated. In our investigation, both the proposed methods and obtained approximations can help many authors investigate several nonlinear oscillations in different plasma models and fluid mechanics.http://dx.doi.org/10.1063/5.0103138 |
| spellingShingle | Weaam Alhejaili Alvaro H. Salas S. A. El-Tantawy Approximate solution to a generalized Van der Pol equation arising in plasma oscillations AIP Advances |
| title | Approximate solution to a generalized Van der Pol equation arising in plasma oscillations |
| title_full | Approximate solution to a generalized Van der Pol equation arising in plasma oscillations |
| title_fullStr | Approximate solution to a generalized Van der Pol equation arising in plasma oscillations |
| title_full_unstemmed | Approximate solution to a generalized Van der Pol equation arising in plasma oscillations |
| title_short | Approximate solution to a generalized Van der Pol equation arising in plasma oscillations |
| title_sort | approximate solution to a generalized van der pol equation arising in plasma oscillations |
| url | http://dx.doi.org/10.1063/5.0103138 |
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