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The higher accuracy fourth-order IADE algorithm

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

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Official URL: http://dx.doi.org/10.1155/2013/236548

Abstract

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

Item Type:Article
Uncontrolled Keywords:algorithm, higher accuracy, heat equation
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:50499
Deposited By: Siti Nor Hashidah Zakaria
Deposited On:02 Dec 2015 10:09
Last Modified:14 Oct 2018 16:37

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