On the convergence of a coupling successive approximation method for solving Duffing equation
General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2014-08-01
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| Series: | Vietnam Journal of Mechanics |
| Subjects: | |
| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/4843 |
| _version_ | 1826575950468349952 |
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| author | Dao Huy Bich Nguyen Dang Bich |
| author_facet | Dao Huy Bich Nguyen Dang Bich |
| author_sort | Dao Huy Bich |
| collection | DOAJ |
| description |
General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive approximation method (CSAM) has been proposed by the authors.In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving.Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM.
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| first_indexed | 2025-03-14T13:22:50Z |
| format | Article |
| id | doaj.art-81de1b74cfa6423884db22faf37e8868 |
| institution | Directory Open Access Journal |
| issn | 0866-7136 2815-5882 |
| language | English |
| last_indexed | 2025-03-14T13:22:50Z |
| publishDate | 2014-08-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj.art-81de1b74cfa6423884db22faf37e88682025-02-28T11:01:22ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822014-08-0136310.15625/0866-7136/36/3/4843On the convergence of a coupling successive approximation method for solving Duffing equationDao Huy Bich0Nguyen Dang Bich1Hanoi University of Science, VNU, VietnamInstitute for Building Science and Technology (IBST), Hanoi, Vietnam General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive approximation method (CSAM) has been proposed by the authors.In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving.Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM. https://vjs.ac.vn/index.php/vjmech/article/view/4843General Duffing equationcoupling successive approximation methodconvergencecomplex valued solutionchaotic solution |
| spellingShingle | Dao Huy Bich Nguyen Dang Bich On the convergence of a coupling successive approximation method for solving Duffing equation Vietnam Journal of Mechanics General Duffing equation coupling successive approximation method convergence complex valued solution chaotic solution |
| title | On the convergence of a coupling successive approximation method for solving Duffing equation |
| title_full | On the convergence of a coupling successive approximation method for solving Duffing equation |
| title_fullStr | On the convergence of a coupling successive approximation method for solving Duffing equation |
| title_full_unstemmed | On the convergence of a coupling successive approximation method for solving Duffing equation |
| title_short | On the convergence of a coupling successive approximation method for solving Duffing equation |
| title_sort | on the convergence of a coupling successive approximation method for solving duffing equation |
| topic | General Duffing equation coupling successive approximation method convergence complex valued solution chaotic solution |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/4843 |
| work_keys_str_mv | AT daohuybich ontheconvergenceofacouplingsuccessiveapproximationmethodforsolvingduffingequation AT nguyendangbich ontheconvergenceofacouplingsuccessiveapproximationmethodforsolvingduffingequation |