An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation
In this paper, we apply He's variational iteration method (VIM) and the Adomian decomposition method (ADM) to approximate the solution of Duffing-Van Der Pol equation (DVP). In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational...
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Mosul University
2013-07-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_163482_0a6017999bf786fbf9dfe5eaaa28d518.pdf |
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| author | Ann Al-Sawoor Merna Samarchi |
| author_facet | Ann Al-Sawoor Merna Samarchi |
| author_sort | Ann Al-Sawoor |
| collection | DOAJ |
| description | In this paper, we apply He's variational iteration method (VIM) and the Adomian decomposition method (ADM) to approximate the solution of Duffing-Van Der Pol equation (DVP). In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons of the two series solutions with the classical Runge-Kutta order four RK45 method show that the VIM is a powerful method for the solution of nonlinear equations. The convergent of He's variational iteration method to this equation is also considered. |
| format | Article |
| id | doaj-art-1d121bc99b6b437fbd25d24d2d62c4a6 |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-1d121bc99b6b437fbd25d24d2d62c4a62025-08-20T02:01:43ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902013-07-0110215316310.33899/csmj.2013.163482163482An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol EquationAnn Al-Sawoor0Merna Samarchi1College of Computer Sciences and Mathematics University of Mosul, Mosul, IraqCollege of Computer Sciences and Mathematics University of Mosul, Mosul, IraqIn this paper, we apply He's variational iteration method (VIM) and the Adomian decomposition method (ADM) to approximate the solution of Duffing-Van Der Pol equation (DVP). In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons of the two series solutions with the classical Runge-Kutta order four RK45 method show that the VIM is a powerful method for the solution of nonlinear equations. The convergent of He's variational iteration method to this equation is also considered.https://csmj.mosuljournals.com/article_163482_0a6017999bf786fbf9dfe5eaaa28d518.pdfhe's variational iteration methodadomian decomposition methodduffing-van der pol equationrunge-kutta order fourapproximate solution |
| spellingShingle | Ann Al-Sawoor Merna Samarchi An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation Al-Rafidain Journal of Computer Sciences and Mathematics he's variational iteration method adomian decomposition method duffing-van der pol equation runge-kutta order four approximate solution |
| title | An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation |
| title_full | An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation |
| title_fullStr | An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation |
| title_full_unstemmed | An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation |
| title_short | An Application of He's Variational Iteration Method for Solving Duffing - Van Der Pol Equation |
| title_sort | application of he s variational iteration method for solving duffing van der pol equation |
| topic | he's variational iteration method adomian decomposition method duffing-van der pol equation runge-kutta order four approximate solution |
| url | https://csmj.mosuljournals.com/article_163482_0a6017999bf786fbf9dfe5eaaa28d518.pdf |
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