Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems
<p>In this research, the application of the homotopy perturbation method to solve nonlinear Equations arising in oscillatory systems is investigated. In this way, the performance of the Homotopy Perturbation Method (HPM) is compared with the numerical methods to find the solutions of nonlinear...
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| Format: | Article |
| Language: | English |
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Islamic Azad University-Isfahan (Khorasgan) Branch
2025-01-01
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| Series: | International Journal of Advanced Design and Manufacturing Technology |
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| Online Access: | https://sanad.iau.ir/journal/admt/Article/873801 |
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| author | Mohammadjavad Mahmoodabadi Neda Amiri |
| author_facet | Mohammadjavad Mahmoodabadi Neda Amiri |
| author_sort | Mohammadjavad Mahmoodabadi |
| collection | DOAJ |
| description | <p>In this research, the application of the homotopy perturbation method to solve nonlinear Equations arising in oscillatory systems is investigated. In this way, the performance of the Homotopy Perturbation Method (HPM) is compared with the numerical methods to find the solutions of nonlinear Equations in the vibration field. To this end, the Duffing–Holmes oscillatory model with nonlinear terms is regarded and solved by the HPM method. In order to validate the obtained solution by the HPM, the answers are compared with those of numerical methods. The results clearly depict that the homotopy perturbation method, without needing to small parameters, could present the answers near to the exact solutions and also to the numerical one.</p> |
| format | Article |
| id | doaj-art-826a1445a022446080dacd820e5f4049 |
| institution | Kabale University |
| issn | 2252-0406 2383-4447 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Islamic Azad University-Isfahan (Khorasgan) Branch |
| record_format | Article |
| series | International Journal of Advanced Design and Manufacturing Technology |
| spelling | doaj-art-826a1445a022446080dacd820e5f40492025-01-25T12:25:37ZengIslamic Azad University-Isfahan (Khorasgan) BranchInternational Journal of Advanced Design and Manufacturing Technology2252-04062383-44472025-01-011742933Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory SystemsMohammadjavad MahmoodabadiNeda Amiri<p>In this research, the application of the homotopy perturbation method to solve nonlinear Equations arising in oscillatory systems is investigated. In this way, the performance of the Homotopy Perturbation Method (HPM) is compared with the numerical methods to find the solutions of nonlinear Equations in the vibration field. To this end, the Duffing–Holmes oscillatory model with nonlinear terms is regarded and solved by the HPM method. In order to validate the obtained solution by the HPM, the answers are compared with those of numerical methods. The results clearly depict that the homotopy perturbation method, without needing to small parameters, could present the answers near to the exact solutions and also to the numerical one.</p>https://sanad.iau.ir/journal/admt/Article/873801duffing-holmes model homotopy perturbation method nonlinear equations oscillatory systems |
| spellingShingle | Mohammadjavad Mahmoodabadi Neda Amiri Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems International Journal of Advanced Design and Manufacturing Technology duffing-holmes model homotopy perturbation method nonlinear equations oscillatory systems |
| title | Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems |
| title_full | Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems |
| title_fullStr | Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems |
| title_full_unstemmed | Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems |
| title_short | Application of the Homotopy Perturbation Method to Solve Nonlinear Equations Arising in Oscillatory Systems |
| title_sort | application of the homotopy perturbation method to solve nonlinear equations arising in oscillatory systems |
| topic | duffing-holmes model homotopy perturbation method nonlinear equations oscillatory systems |
| url | https://sanad.iau.ir/journal/admt/Article/873801 |
| work_keys_str_mv | AT mohammadjavadmahmoodabadi applicationofthehomotopyperturbationmethodtosolvenonlinearequationsarisinginoscillatorysystems AT nedaamiri applicationofthehomotopyperturbationmethodtosolvenonlinearequationsarisinginoscillatorysystems |