A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom
A novel technique is proposed for finding an approximate solution of the strongly nonlinear ordinary differential equation for the charged damped pendulum with one degree of freedom. The method relies on a transformation of the governing nonlinear differential equation that keeps unchanged the order...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000554 |
| _version_ | 1797390384296361984 |
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| author | M.H. Zekry G.M. Moatimid M.S. Abou-Dina A.F. Ghaleb |
| author_facet | M.H. Zekry G.M. Moatimid M.S. Abou-Dina A.F. Ghaleb |
| author_sort | M.H. Zekry |
| collection | DOAJ |
| description | A novel technique is proposed for finding an approximate solution of the strongly nonlinear ordinary differential equation for the charged damped pendulum with one degree of freedom. The method relies on a transformation of the governing nonlinear differential equation that keeps unchanged the order of the highest derivative, in conjunction with a modified homotopy perturbation technique (MHPM). Only quadratic damping is considered for the numerical computations. To validate the used technique, the obtained results are compared to those arising from a numerical solution by Runge–Kutta of the fourth order (RK4) and by finite differences (FD). Good agreement between the two solutions is reached when quadratic damping is suppressed. In the presence of damping, agreement takes place only for a rather limited range of times. Plots of the analytical solutions are provided for both cases. The proposed method may be used to analyze a wide class of nonlinear differential equations. |
| first_indexed | 2024-03-08T23:10:56Z |
| format | Article |
| id | doaj.art-ec880a2d296f411da713a00b22d2c0ae |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:56Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-ec880a2d296f411da713a00b22d2c0ae2023-12-15T07:26:44ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100542A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedomM.H. Zekry0G.M. Moatimid1M.S. Abou-Dina2A.F. Ghaleb3Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt; Corresponding author.Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptA novel technique is proposed for finding an approximate solution of the strongly nonlinear ordinary differential equation for the charged damped pendulum with one degree of freedom. The method relies on a transformation of the governing nonlinear differential equation that keeps unchanged the order of the highest derivative, in conjunction with a modified homotopy perturbation technique (MHPM). Only quadratic damping is considered for the numerical computations. To validate the used technique, the obtained results are compared to those arising from a numerical solution by Runge–Kutta of the fourth order (RK4) and by finite differences (FD). Good agreement between the two solutions is reached when quadratic damping is suppressed. In the presence of damping, agreement takes place only for a rather limited range of times. Plots of the analytical solutions are provided for both cases. The proposed method may be used to analyze a wide class of nonlinear differential equations.http://www.sciencedirect.com/science/article/pii/S2666818123000554Nonlinear differential equationSpherical charged pendulumModified homotopy perturbation method |
| spellingShingle | M.H. Zekry G.M. Moatimid M.S. Abou-Dina A.F. Ghaleb A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom Partial Differential Equations in Applied Mathematics Nonlinear differential equation Spherical charged pendulum Modified homotopy perturbation method |
| title | A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| title_full | A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| title_fullStr | A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| title_full_unstemmed | A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| title_short | A novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| title_sort | novel approach for an approximate solution of a nonlinear equation of charged damped oscillator with one degree of freedom |
| topic | Nonlinear differential equation Spherical charged pendulum Modified homotopy perturbation method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000554 |
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