Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity
We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximat...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/649748 |
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| _version_ | 1832566928033447936 |
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| author | Najeeb Alam Khan Muhammad Jamil Asmat Ara |
| author_facet | Najeeb Alam Khan Muhammad Jamil Asmat Ara |
| author_sort | Najeeb Alam Khan |
| collection | DOAJ |
| description | We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique. |
| format | Article |
| id | doaj-art-ea1306d0a41a4e5a87183d2975bb9d8b |
| 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-ea1306d0a41a4e5a87183d2975bb9d8b2025-02-03T01:02:49ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/649748649748Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with DiscontinuityNajeeb Alam Khan0Muhammad Jamil1Asmat Ara2Department of Mathematics, University of Karachi, Karachi 75270, PakistanAbdul Salam School of Mathematical Sciences, GC University, Lahore, PakistanDepartment of Mathematics, University of Karachi, Karachi 75270, PakistanWe applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.http://dx.doi.org/10.1155/2011/649748 |
| spellingShingle | Najeeb Alam Khan Muhammad Jamil Asmat Ara Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity International Journal of Differential Equations |
| title | Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity |
| title_full | Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity |
| title_fullStr | Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity |
| title_full_unstemmed | Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity |
| title_short | Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity |
| title_sort | multiple parameter hamiltonian approach for higher accurate approximations of a nonlinear oscillator with discontinuity |
| url | http://dx.doi.org/10.1155/2011/649748 |
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