Solutions of the Force-Free Duffing-van der Pol Oscillator Equation
A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/852919 |
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| _version_ | 1832561694665080832 |
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| author | Najeeb Alam Khan Muhammad Jamil Syed Anwar Ali Nadeem Alam Khan |
| author_facet | Najeeb Alam Khan Muhammad Jamil Syed Anwar Ali Nadeem Alam Khan |
| author_sort | Najeeb Alam Khan |
| collection | DOAJ |
| description | A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution. |
| format | Article |
| id | doaj-art-2f387d6e9ed3481b93fa36c57a93fdca |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-2f387d6e9ed3481b93fa36c57a93fdca2025-02-03T01:24:28ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/852919852919Solutions of the Force-Free Duffing-van der Pol Oscillator EquationNajeeb Alam Khan0Muhammad Jamil1Syed Anwar Ali2Nadeem Alam Khan3Department of Mathematics, University of Karachi, Karachi 75270, PakistanAbdul Salam School of Mathematical Sciences, GC University, Lahore, PakistanDepartment of Mathematics, University of Karachi, Karachi 75270, PakistanDepartment of Mathematics, University of Karachi, Karachi 75270, PakistanA new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.http://dx.doi.org/10.1155/2011/852919 |
| spellingShingle | Najeeb Alam Khan Muhammad Jamil Syed Anwar Ali Nadeem Alam Khan Solutions of the Force-Free Duffing-van der Pol Oscillator Equation International Journal of Differential Equations |
| title | Solutions of the Force-Free Duffing-van der Pol Oscillator Equation |
| title_full | Solutions of the Force-Free Duffing-van der Pol Oscillator Equation |
| title_fullStr | Solutions of the Force-Free Duffing-van der Pol Oscillator Equation |
| title_full_unstemmed | Solutions of the Force-Free Duffing-van der Pol Oscillator Equation |
| title_short | Solutions of the Force-Free Duffing-van der Pol Oscillator Equation |
| title_sort | solutions of the force free duffing van der pol oscillator equation |
| url | http://dx.doi.org/10.1155/2011/852919 |
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