A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems
In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are deri...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/591636 |
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| _version_ | 1832562189501726720 |
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| author | A. Karimi Dizicheh F. Ismail M. Tavassoli Kajani Mohammad Maleki |
| author_facet | A. Karimi Dizicheh F. Ismail M. Tavassoli Kajani Mohammad Maleki |
| author_sort | A. Karimi Dizicheh |
| collection | DOAJ |
| description | In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre
wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate. |
| format | Article |
| id | doaj-art-64edc6398fe6421187f5e3e88c44f47b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-64edc6398fe6421187f5e3e88c44f47b2025-02-03T01:23:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/591636591636A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value ProblemsA. Karimi Dizicheh0F. Ismail1M. Tavassoli Kajani2Mohammad Maleki3Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Khorasgan Branch, Islamic Azad University, Khorasgan, Isfahan, IranSchool of Mathematical Sciences, National University of Malaysia (UKM), 43600 Bangi, Selangor, MalaysiaIn this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.http://dx.doi.org/10.1155/2013/591636 |
| spellingShingle | A. Karimi Dizicheh F. Ismail M. Tavassoli Kajani Mohammad Maleki A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems Journal of Applied Mathematics |
| title | A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems |
| title_full | A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems |
| title_fullStr | A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems |
| title_full_unstemmed | A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems |
| title_short | A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems |
| title_sort | legendre wavelet spectral collocation method for solving oscillatory initial value problems |
| url | http://dx.doi.org/10.1155/2013/591636 |
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