Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach
In this paper, the coupled homotopy-variational approach (CHVA) based on combining homotopy with the variational approach is applied to solve the nonlinear Duffing equation, and new frequency- amplitude relationships are obtained. The coupled method works very well for the entire range of initial am...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-07-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821006220 |
| _version_ | 1811344557490569216 |
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| author | G.M. Ismail M. Abul-Ez M. Zayed N.M. Farea |
| author_facet | G.M. Ismail M. Abul-Ez M. Zayed N.M. Farea |
| author_sort | G.M. Ismail |
| collection | DOAJ |
| description | In this paper, the coupled homotopy-variational approach (CHVA) based on combining homotopy with the variational approach is applied to solve the nonlinear Duffing equation, and new frequency- amplitude relationships are obtained. The coupled method works very well for the entire range of initial amplitudes and calculates higher-order approximations. The results are compared with those obtained using other known analytical and numerical methods to substantiate the accuracy and efficiency of the approximate analytical approach. The method provides better results than other existing methods. The advantage of the coupled method is that the current second order approximations almost coincide with the corresponding exact solutions. Thus, the presented CHVA could be applied to other strongly nonlinear differential equations. |
| first_indexed | 2024-04-13T19:49:58Z |
| format | Article |
| id | doaj.art-54a95e7cd7d6442189bacd5ec66f3009 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-13T19:49:58Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-54a95e7cd7d6442189bacd5ec66f30092022-12-22T02:32:35ZengElsevierAlexandria Engineering Journal1110-01682022-07-0161750515058Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approachG.M. Ismail0M. Abul-Ez1M. Zayed2N.M. Farea3Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt; Department of Mathematics, Faculty of Science, Islamic University of Madinah, 42351 Madinah, Saudi Arabia; Corresponding author at: Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, EgyptMathematics Department, College of Science, King Khalid University, Abha, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Sohag University, Sohag 82524, EgyptIn this paper, the coupled homotopy-variational approach (CHVA) based on combining homotopy with the variational approach is applied to solve the nonlinear Duffing equation, and new frequency- amplitude relationships are obtained. The coupled method works very well for the entire range of initial amplitudes and calculates higher-order approximations. The results are compared with those obtained using other known analytical and numerical methods to substantiate the accuracy and efficiency of the approximate analytical approach. The method provides better results than other existing methods. The advantage of the coupled method is that the current second order approximations almost coincide with the corresponding exact solutions. Thus, the presented CHVA could be applied to other strongly nonlinear differential equations.http://www.sciencedirect.com/science/article/pii/S1110016821006220Nonlinear vibrationApproximate solutionsHomotopy perturbation methodVariational iteration methodNonlinear stiffnessesDuffing equation |
| spellingShingle | G.M. Ismail M. Abul-Ez M. Zayed N.M. Farea Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach Alexandria Engineering Journal Nonlinear vibration Approximate solutions Homotopy perturbation method Variational iteration method Nonlinear stiffnesses Duffing equation |
| title | Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach |
| title_full | Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach |
| title_fullStr | Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach |
| title_full_unstemmed | Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach |
| title_short | Analytical accurate solutions of nonlinear oscillator systems via coupled homotopy-variational approach |
| title_sort | analytical accurate solutions of nonlinear oscillator systems via coupled homotopy variational approach |
| topic | Nonlinear vibration Approximate solutions Homotopy perturbation method Variational iteration method Nonlinear stiffnesses Duffing equation |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821006220 |
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