The higher accuracy fourth-order IADE algorithm
This study develops the novel fourth-order iterative alternating decomposition explicit (IADE)method of Mitchell and Fair weather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions.The higher order finite difference scheme is developed...
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my.utm.504992018-10-14T08:37:00Z http://eprints.utm.my/id/eprint/50499/ The higher accuracy fourth-order IADE algorithm Abu Mansor, N. Zulkifle, Ahmad Kamal Alias, Norma Hasan, Mohammad Khatim Boyce, M. J. N. QA Mathematics This study develops the novel fourth-order iterative alternating decomposition explicit (IADE)method of Mitchell and Fair weather (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 Fair weather 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 bench marked fourth-order classical iterative methods, namely, the Jacobi (JAC4), the Gauss-Seidel (GS4), and the successive over-relaxation (SOR4) methods Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/50499/1/NormaAlias2013_Thehigheraccuracyfourth-order.pdf Abu Mansor, N. and Zulkifle, Ahmad Kamal and Alias, Norma and Hasan, Mohammad Khatim and Boyce, M. J. N. (2013) The higher accuracy fourth-order IADE algorithm. Journal of Applied Mathematics . pp. 1-13. ISSN 1110-757X http://dx.doi.org/10.1155/2013/236548 DOI: 10.1155/2013/236548 |
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This study develops the novel fourth-order iterative alternating decomposition explicit (IADE)method of Mitchell and Fair weather (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 Fair weather 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 bench marked fourth-order classical iterative methods, namely, the Jacobi (JAC4), the Gauss-Seidel (GS4), and the successive over-relaxation (SOR4) methods |
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Article |
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Abu Mansor, N. Zulkifle, Ahmad Kamal Alias, Norma Hasan, Mohammad Khatim Boyce, M. J. N. |
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Abu Mansor, N. Zulkifle, Ahmad Kamal Alias, Norma Hasan, Mohammad Khatim Boyce, M. J. N. |
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Abu Mansor, N. |
title |
The higher accuracy fourth-order IADE algorithm |
title_short |
The higher accuracy fourth-order IADE algorithm |
title_full |
The higher accuracy fourth-order IADE algorithm |
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The higher accuracy fourth-order IADE algorithm |
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The higher accuracy fourth-order IADE algorithm |
title_sort |
higher accuracy fourth-order iade algorithm |
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Hindawi Publishing Corporation |
publishDate |
2013 |
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http://eprints.utm.my/id/eprint/50499/1/NormaAlias2013_Thehigheraccuracyfourth-order.pdf http://eprints.utm.my/id/eprint/50499/ http://dx.doi.org/10.1155/2013/236548 |
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