The Higher Accuracy Fourth-Order IADE Algorithm
Joint Authors
Zulkifle, A. K.
Boyce, M. J. N.
Alias, N.
Hasan, M. K.
Abu Mansor, N.
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Abu Mansor, N.& Zulkifle, A. K.& Alias, N.& Hasan, M. K.& Boyce, M. J. N.. 2013. The Higher Accuracy Fourth-Order IADE Algorithm. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-456169
Modern Language Association (MLA)
Abu Mansor, N.…[et al.]. The Higher Accuracy Fourth-Order IADE Algorithm. Journal of Applied Mathematics No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-456169
American Medical Association (AMA)
Abu Mansor, N.& Zulkifle, A. K.& Alias, N.& Hasan, M. K.& Boyce, M. J. N.. The Higher Accuracy Fourth-Order IADE Algorithm. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-456169
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456169