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Journal of Applied MathematicsVolume 2013 2013, Article ID 236548, 13 pages

Research Article

College of Engineering, Universiti Tenaga Nasional, Jalan Ikram-UNITEN, 43000 Kajang, Selangor, Malaysia

Ibnu Sina Institute of Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 21 May 2013; Accepted 26 July 2013

Academic Editor: Juan Manuel Peña

Copyright © 2013 N. Abu Mansor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.





Author: N. Abu Mansor, A. K. Zulkifle, N. Alias, M. K. Hasan, and M. J. N. Boyce

Source: https://www.hindawi.com/



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