The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators
The Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyze five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Ite...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/7487851 |
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| author | D. V. Hieu N. Q. Hai D. T. Hung |
| author_facet | D. V. Hieu N. Q. Hai D. T. Hung |
| author_sort | D. V. Hieu |
| collection | DOAJ |
| description | The Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyze five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th-Order Runge-Kutta Method, and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully applied to a lot of practical engineering and physical problems. |
| format | Article |
| id | doaj-art-3c2518f9ee9d403c8e3c5831679bfe5b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3c2518f9ee9d403c8e3c5831679bfe5b2025-02-03T05:43:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/74878517487851The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear OscillatorsD. V. Hieu0N. Q. Hai1D. T. Hung2Thai Nguyen University of Technology, Thai Nguyen, VietnamHanoi Architectural University, Ha Noi, VietnamThai Nguyen University of Technology, Thai Nguyen, VietnamThe Equivalent Linearization Method (ELM) with a weighted averaging is applied to analyze five undamped oscillator systems with nonlinearities. The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th-Order Runge-Kutta Method, and the exact ones. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully applied to a lot of practical engineering and physical problems.http://dx.doi.org/10.1155/2018/7487851 |
| spellingShingle | D. V. Hieu N. Q. Hai D. T. Hung The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators Journal of Applied Mathematics |
| title | The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators |
| title_full | The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators |
| title_fullStr | The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators |
| title_full_unstemmed | The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators |
| title_short | The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators |
| title_sort | equivalent linearization method with a weighted averaging for solving undamped nonlinear oscillators |
| url | http://dx.doi.org/10.1155/2018/7487851 |
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