An efficient iterative scheme using family of chebyshev's operations
This paper presents an efficient iterative method originated from the family of Chebyshev's operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavele...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Mathematical Problems in Engineering
2015
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| Online Access: | http://eprints.um.edu.my/13742/1/An_Efficient_Iterative_Scheme_Using_Family_of_Chebyshev.pdf |
| _version_ | 1796946628350836736 |
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| author | Mahdavi, S.H. Razak, H.A. |
| author_facet | Mahdavi, S.H. Razak, H.A. |
| author_sort | Mahdavi, S.H. |
| collection | UM |
| description | This paper presents an efficient iterative method originated from the family of Chebyshev's operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev's iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems. |
| first_indexed | 2024-03-06T05:34:40Z |
| format | Article |
| id | um.eprints-13742 |
| institution | Universiti Malaya |
| language | English |
| last_indexed | 2024-03-06T05:34:40Z |
| publishDate | 2015 |
| publisher | Mathematical Problems in Engineering |
| record_format | dspace |
| spelling | um.eprints-137422015-07-22T01:43:45Z http://eprints.um.edu.my/13742/ An efficient iterative scheme using family of chebyshev's operations Mahdavi, S.H. Razak, H.A. T Technology (General) TA Engineering (General). Civil engineering (General) This paper presents an efficient iterative method originated from the family of Chebyshev's operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev's iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems. Mathematical Problems in Engineering 2015 Article PeerReviewed application/pdf en http://eprints.um.edu.my/13742/1/An_Efficient_Iterative_Scheme_Using_Family_of_Chebyshev.pdf Mahdavi, S.H. and Razak, H.A. (2015) An efficient iterative scheme using family of chebyshev's operations. Mathematical Problems in Engineering. p. 10. ISSN 1024-123X, DOI https://doi.org/10.1155/2015/205295 <https://doi.org/10.1155/2015/205295>. http://www.hindawi.com/journals/mpe/2015/205295/ Doi 10.1155/2015/205295 |
| spellingShingle | T Technology (General) TA Engineering (General). Civil engineering (General) Mahdavi, S.H. Razak, H.A. An efficient iterative scheme using family of chebyshev's operations |
| title | An efficient iterative scheme using family of chebyshev's operations |
| title_full | An efficient iterative scheme using family of chebyshev's operations |
| title_fullStr | An efficient iterative scheme using family of chebyshev's operations |
| title_full_unstemmed | An efficient iterative scheme using family of chebyshev's operations |
| title_short | An efficient iterative scheme using family of chebyshev's operations |
| title_sort | efficient iterative scheme using family of chebyshev s operations |
| topic | T Technology (General) TA Engineering (General). Civil engineering (General) |
| url | http://eprints.um.edu.my/13742/1/An_Efficient_Iterative_Scheme_Using_Family_of_Chebyshev.pdf |
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