About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 867598, 14 pages
http://dx.doi.org/10.1155/2012/867598
Research Article

Convergence Analysis of the Preconditioned Group Splitting Methods in Boundary Value Problems

School of Mathematical Sciences, Universitiy Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

Received 17 May 2012; Accepted 12 July 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Norhashidah Hj. Mohd Ali and Abdulkafi Mohammed Saeed. 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.

Linked References

  1. A. R. Abdullah, “The four point explicit decoupled group (EDG) method: a fast poisson solver,” International Journal of Computer Mathematics, vol. 38, pp. 61–70, 1991.
  2. D. J. Evans and W. S. Yousif, “The implementation of the explicit block iterative methods on the balance 8000 parallel computer,” Parallel Computing, vol. 16, no. 1, pp. 81–97, 1990. View at Scopus
  3. M. M. Martins, W. S. Yousif, and D. J. Evans, “Explicit group AOR method for solving elliptic partial differential equations,” Neural, Parallel & Scientific Computations, vol. 10, no. 4, pp. 411–422, 2002.
  4. M. Othman and A. R. Abdullah, “Efficient four points modified explicit group Poisson solver,” International Journal of Computer Mathematics, vol. 76, no. 2, pp. 203–217, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. W. S. Yousif and D. J. Evans, “Explicit group over-relaxation methods for solving elliptic partial differential equations,” Mathematics and Computers in Simulation, vol. 28, no. 6, pp. 453–466, 1986. View at Publisher · View at Google Scholar · View at Scopus
  6. N. H. M. Ali and K. F. Ng, “Modified explicit decoupled group method in the solution of 2-D elliptic PDEs,” in Proceedings of the 12th WSEAS International Conference on Applied Mathematics, pp. 162–167, Cairo, Egypt, December2007.
  7. N. H. M. Ali and K. F. Ng, “A new iterative elliptic PDE solver on a distributed PC cluster,” in Proceedings of the 9th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT'08), pp. 47–53, Dunedin, New Zealand, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. A. D. Gunawardena, S. K. Jain, and L. Snyder, “Modified iterative methods for consistent linear systems,” Linear Algebra and Its Applications, vol. 154–156, pp. 123–143, 1991. View at Publisher · View at Google Scholar · View at Scopus
  9. S. C. Lee, Point and group iterative method accelerated techniques for solving the Poisson problem [M.S. thesis], USM, Penang, Malaysia, 2006.
  10. M. M. Martins, D. J. Evans, and W. Yousif, “Further results on the preconditioned SOR method,” International Journal of Computer Mathematics, vol. 77, no. 4, pp. 603–610, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Usui, T. Kohno, and H. Niki, “On the preconditioned SOR method,” International Journal of Computer Mathematics, vol. 59, no. 1, pp. 123–130, 1995. View at Publisher · View at Google Scholar
  12. A. M. Saeed and N. H. M. Ali, “Preconditioned (I+S¯) group iterative methods on rotated grids,” European Journal of Scientific Research, vol. 37, no. 2, pp. 278–287, 2009. View at Scopus
  13. A. M. Saeed and N. H. M. Ali, “Preconditioned modified explicit decoupled group method in the solution of elliptic PDEs,” Applied Mathematical Sciences, vol. 4, no. 21–24, pp. 1165–1181, 2010. View at Scopus
  14. A. M. Saeed and N. H. M. Ali, “On the convergence of the preconditioned group rotated iterative methods in the solution of elliptic PDEs,” Applied Mathematics & Information Sciences, vol. 5, no. 1, pp. 65–73, 2011.
  15. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1962.
  16. W. S. Yousif and D. J. Evans, “Explicit de-coupled group iterative methods and their parallel implementation,” Parallel Algorithms and Applications, vol. 7, no. 1-2, pp. 53–71, 1995. View at Publisher · View at Google Scholar
  17. Y. G. Saridakis, “Generalized consistent orderings and the accelerated overrelaxation method,” BIT Numerical Mathematics, vol. 26, no. 3, pp. 369–376, 1986. View at Publisher · View at Google Scholar · View at Scopus