Nonlinear Mathieu Equation and its Approximation Without a Small Parameter
In this paper, the linear and nonlinear Mathieu equations without a small parameter are considered, which cannot be solved by the perturbation techniques. However, using the variational iteration method, their periodic solutions can be readily obtained with high accuracy. In addition, some special c...
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| Format: | Article |
| Language: | English |
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Institute of Fundamental Technological Research
2015-06-01
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| Series: | Engineering Transactions |
| Online Access: | https://et.ippt.pan.pl/index.php/et/article/view/507 |
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| author | Ji-Huan He |
| author_facet | Ji-Huan He |
| author_sort | Ji-Huan He |
| collection | DOAJ |
| description | In this paper, the linear and nonlinear Mathieu equations without a small parameter are considered, which cannot be solved by the perturbation techniques. However, using the variational iteration method, their periodic solutions can be readily obtained with high accuracy. In addition, some special cases have been discussed, where the perturbation solutions are meaningless even when there exists a small parameter. |
| format | Article |
| id | doaj-art-f4aaf8c7a90c48f68f7c5acb42e670e3 |
| institution | Matheson Library |
| issn | 0867-888X 2450-8071 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Institute of Fundamental Technological Research |
| record_format | Article |
| series | Engineering Transactions |
| spelling | doaj-art-f4aaf8c7a90c48f68f7c5acb42e670e32025-07-11T05:05:33ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80712015-06-01501-210.24423/engtrans.507.2002Nonlinear Mathieu Equation and its Approximation Without a Small ParameterJi-Huan He0Shanghai Donghua UniversityIn this paper, the linear and nonlinear Mathieu equations without a small parameter are considered, which cannot be solved by the perturbation techniques. However, using the variational iteration method, their periodic solutions can be readily obtained with high accuracy. In addition, some special cases have been discussed, where the perturbation solutions are meaningless even when there exists a small parameter.https://et.ippt.pan.pl/index.php/et/article/view/507 |
| spellingShingle | Ji-Huan He Nonlinear Mathieu Equation and its Approximation Without a Small Parameter Engineering Transactions |
| title | Nonlinear Mathieu Equation and its Approximation Without a Small Parameter |
| title_full | Nonlinear Mathieu Equation and its Approximation Without a Small Parameter |
| title_fullStr | Nonlinear Mathieu Equation and its Approximation Without a Small Parameter |
| title_full_unstemmed | Nonlinear Mathieu Equation and its Approximation Without a Small Parameter |
| title_short | Nonlinear Mathieu Equation and its Approximation Without a Small Parameter |
| title_sort | nonlinear mathieu equation and its approximation without a small parameter |
| url | https://et.ippt.pan.pl/index.php/et/article/view/507 |
| work_keys_str_mv | AT jihuanhe nonlinearmathieuequationanditsapproximationwithoutasmallparameter |