The Higher Accuracy Fourth-Order IADE Algorithm
This study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. The higher-order finite difference scheme is develope...
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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/10.1155/2013/236548 |
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| author | N. Abu Mansor A. K. Zulkifle N. Alias M. K. Hasan M. J. N. Boyce |
| author_facet | N. Abu Mansor A. K. Zulkifle N. Alias M. K. Hasan M. J. N. Boyce |
| author_sort | N. Abu Mansor |
| collection | DOAJ |
| description | This study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. The higher-order finite difference scheme is developed by representing the spatial derivative in the heat equation with the fourth-order finite difference Crank-Nicolson approximation. This leads to the formation of pentadiagonal matrices in the systems of linear equations. The algorithm also employs the higher accuracy of the Mitchell and Fairweather variant. Despite the scheme’s higher computational complexity, experimental results show that it is not only capable of enhancing the accuracy of the original corresponding method of second-order (IADEMF2), but its solutions are also in very much agreement with the exact solutions. Besides, it is unconditionally stable and has proven to be convergent. The IADEMF4 is also found to be more accurate, more efficient, and has better rate of convergence than the benchmarked fourth-order classical iterative methods, namely, the Jacobi (JAC4), the Gauss-Seidel (GS4), and the successive over-relaxation (SOR4) methods. |
| format | Article |
| id | doaj-art-b7dcf9da32d74a959cb85b19b5fd7f76 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b7dcf9da32d74a959cb85b19b5fd7f762025-08-20T02:19:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/236548236548The Higher Accuracy Fourth-Order IADE AlgorithmN. Abu Mansor0A. K. Zulkifle1N. Alias2M. K. Hasan3M. J. N. Boyce4College of Engineering, Universiti Tenaga Nasional, Jalan Ikram-UNITEN, 43000 Kajang, Selangor, MalaysiaCollege of Engineering, Universiti Tenaga Nasional, Jalan Ikram-UNITEN, 43000 Kajang, Selangor, MalaysiaIbnu Sina Institute of Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 Skudai, Johor, MalaysiaFaculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaCollege of Engineering, Universiti Tenaga Nasional, Jalan Ikram-UNITEN, 43000 Kajang, Selangor, MalaysiaThis study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. The higher-order finite difference scheme is developed by representing the spatial derivative in the heat equation with the fourth-order finite difference Crank-Nicolson approximation. This leads to the formation of pentadiagonal matrices in the systems of linear equations. The algorithm also employs the higher accuracy of the Mitchell and Fairweather variant. Despite the scheme’s higher computational complexity, experimental results show that it is not only capable of enhancing the accuracy of the original corresponding method of second-order (IADEMF2), but its solutions are also in very much agreement with the exact solutions. Besides, it is unconditionally stable and has proven to be convergent. The IADEMF4 is also found to be more accurate, more efficient, and has better rate of convergence than the benchmarked fourth-order classical iterative methods, namely, the Jacobi (JAC4), the Gauss-Seidel (GS4), and the successive over-relaxation (SOR4) methods.http://dx.doi.org/10.1155/2013/236548 |
| spellingShingle | N. Abu Mansor A. K. Zulkifle N. Alias M. K. Hasan M. J. N. Boyce The Higher Accuracy Fourth-Order IADE Algorithm Journal of Applied Mathematics |
| title | The Higher Accuracy Fourth-Order IADE Algorithm |
| title_full | The Higher Accuracy Fourth-Order IADE Algorithm |
| title_fullStr | The Higher Accuracy Fourth-Order IADE Algorithm |
| title_full_unstemmed | The Higher Accuracy Fourth-Order IADE Algorithm |
| title_short | The Higher Accuracy Fourth-Order IADE Algorithm |
| title_sort | higher accuracy fourth order iade algorithm |
| url | http://dx.doi.org/10.1155/2013/236548 |
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