Numerical solution of fractional Mathieu equations by using block-pulse wavelets
In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Capu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-12-01
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| Series: | Journal of Ocean Engineering and Science |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468013319300439 |
| _version_ | 1828471162928103424 |
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| author | P. Pirmohabbati A.H. Refahi Sheikhani H. Saberi Najafi A. Abdolahzadeh Ziabari |
| author_facet | P. Pirmohabbati A.H. Refahi Sheikhani H. Saberi Najafi A. Abdolahzadeh Ziabari |
| author_sort | P. Pirmohabbati |
| collection | DOAJ |
| description | In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. Keywords: Block-pulse functions, Fractional calculus, Mathieu differential equation, MSC: 26A33, 93D20, 97N40, 34A08 |
| first_indexed | 2024-12-11T05:06:21Z |
| format | Article |
| id | doaj.art-d3a39c796472478d81c8ed9e226717ce |
| institution | Directory Open Access Journal |
| issn | 2468-0133 |
| language | English |
| last_indexed | 2024-12-11T05:06:21Z |
| publishDate | 2019-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Ocean Engineering and Science |
| spelling | doaj.art-d3a39c796472478d81c8ed9e226717ce2022-12-22T01:20:01ZengElsevierJournal of Ocean Engineering and Science2468-01332019-12-0144299307Numerical solution of fractional Mathieu equations by using block-pulse waveletsP. Pirmohabbati0A.H. Refahi Sheikhani1H. Saberi Najafi2A. Abdolahzadeh Ziabari3Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranCorresponding author.; Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, IranDepartment of physics, Faculty of Science, Lahidjan Branch, Islamic Azad University, Lahidjan, IranIn this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. Keywords: Block-pulse functions, Fractional calculus, Mathieu differential equation, MSC: 26A33, 93D20, 97N40, 34A08http://www.sciencedirect.com/science/article/pii/S2468013319300439 |
| spellingShingle | P. Pirmohabbati A.H. Refahi Sheikhani H. Saberi Najafi A. Abdolahzadeh Ziabari Numerical solution of fractional Mathieu equations by using block-pulse wavelets Journal of Ocean Engineering and Science |
| title | Numerical solution of fractional Mathieu equations by using block-pulse wavelets |
| title_full | Numerical solution of fractional Mathieu equations by using block-pulse wavelets |
| title_fullStr | Numerical solution of fractional Mathieu equations by using block-pulse wavelets |
| title_full_unstemmed | Numerical solution of fractional Mathieu equations by using block-pulse wavelets |
| title_short | Numerical solution of fractional Mathieu equations by using block-pulse wavelets |
| title_sort | numerical solution of fractional mathieu equations by using block pulse wavelets |
| url | http://www.sciencedirect.com/science/article/pii/S2468013319300439 |
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