The higher accuracy fourth-order IADE algorithm

N. Abu Mansor, A. K. Zulkifle, N. Alias, Mohammad Khatim Hasan, M. J N Boyce

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Article number236548
JournalJournal of Applied Mathematics
Volume2013
DOIs
Publication statusPublished - 2013

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Fourth Order
High Accuracy
Decomposition
Decompose
Heat Equation
Pentadiagonal Matrices
Iterative methods
Linear equations
Crank-Nicolson
Computational complexity
Gauss-Seidel
Relaxation Method
Unconditionally Stable
Explicit Methods
Boundary conditions
System of Linear Equations
Decomposition Method
Derivatives
Finite Difference Scheme
Jacobi

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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, 2013, [236548]. https://doi.org/10.1155/2013/236548

The higher accuracy fourth-order IADE algorithm. / Abu Mansor, N.; Zulkifle, A. K.; Alias, N.; Hasan, Mohammad Khatim; Boyce, M. J N.

In: Journal of Applied Mathematics, Vol. 2013, 236548, 2013.

Research output: Contribution to journalArticle

Abu Mansor, N, Zulkifle, AK, Alias, N, Hasan, MK & Boyce, MJN 2013, 'The higher accuracy fourth-order IADE algorithm', Journal of Applied Mathematics, vol. 2013, 236548. https://doi.org/10.1155/2013/236548
Abu Mansor, N. ; Zulkifle, A. K. ; Alias, N. ; Hasan, Mohammad Khatim ; Boyce, M. J N. / The higher accuracy fourth-order IADE algorithm. In: Journal of Applied Mathematics. 2013 ; Vol. 2013.
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