A new approach for solving Duffing equations involving both integral and non-integral forcing terms
In this paper a Legendre wavelet operational matrix of derivative (LWOM) is used to solve the Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions. This operational matrix method together with Gaussian quadrature formula converts the given Duffin...
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| Format: | Article |
| Language: | English |
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Elsevier
2014-09-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447914000410 |
| _version_ | 1818667998925291520 |
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| author | S. Balaji |
| author_facet | S. Balaji |
| author_sort | S. Balaji |
| collection | DOAJ |
| description | In this paper a Legendre wavelet operational matrix of derivative (LWOM) is used to solve the Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions. This operational matrix method together with Gaussian quadrature formula converts the given Duffing equation into system of algebraic equations, which indeed makes computation of solution easier. The applicability and simplicity of the proposed method is demonstrated by some examples and comparison with other recent methods. It is to be noted that, to the best of our knowledge, no wavelet based method applied for solving Duffing equations so far. |
| first_indexed | 2024-12-17T06:29:20Z |
| format | Article |
| id | doaj.art-770ff93bd0bb47e7a81033c1fa35d4da |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-17T06:29:20Z |
| publishDate | 2014-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-770ff93bd0bb47e7a81033c1fa35d4da2022-12-21T22:00:12ZengElsevierAin Shams Engineering Journal2090-44792014-09-015398599010.1016/j.asej.2014.04.001A new approach for solving Duffing equations involving both integral and non-integral forcing termsS. BalajiIn this paper a Legendre wavelet operational matrix of derivative (LWOM) is used to solve the Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions. This operational matrix method together with Gaussian quadrature formula converts the given Duffing equation into system of algebraic equations, which indeed makes computation of solution easier. The applicability and simplicity of the proposed method is demonstrated by some examples and comparison with other recent methods. It is to be noted that, to the best of our knowledge, no wavelet based method applied for solving Duffing equations so far.http://www.sciencedirect.com/science/article/pii/S2090447914000410Duffing equationLegendre waveletOperational matrix of derivativeIntegral and non-integral forcing terms |
| spellingShingle | S. Balaji A new approach for solving Duffing equations involving both integral and non-integral forcing terms Ain Shams Engineering Journal Duffing equation Legendre wavelet Operational matrix of derivative Integral and non-integral forcing terms |
| title | A new approach for solving Duffing equations involving both integral and non-integral forcing terms |
| title_full | A new approach for solving Duffing equations involving both integral and non-integral forcing terms |
| title_fullStr | A new approach for solving Duffing equations involving both integral and non-integral forcing terms |
| title_full_unstemmed | A new approach for solving Duffing equations involving both integral and non-integral forcing terms |
| title_short | A new approach for solving Duffing equations involving both integral and non-integral forcing terms |
| title_sort | new approach for solving duffing equations involving both integral and non integral forcing terms |
| topic | Duffing equation Legendre wavelet Operational matrix of derivative Integral and non-integral forcing terms |
| url | http://www.sciencedirect.com/science/article/pii/S2090447914000410 |
| work_keys_str_mv | AT sbalaji anewapproachforsolvingduffingequationsinvolvingbothintegralandnonintegralforcingterms AT sbalaji newapproachforsolvingduffingequationsinvolvingbothintegralandnonintegralforcingterms |