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Volume 3, Issue 1, February 2014, Page: 1-6
Precondition for Discretized Fractional Boundary Value Problem
I. K. Youssef, Department of Mathematics, Ain Shams University, Cairo, Egypt
A. M. Shukur, Department of Applied Mathematics, University of Technology, Baghdad, Iraq
Received: Jan. 23, 2014;       Published: Feb. 20, 2014
DOI: 10.11648/j.pamj.20140301.11      View  3353      Downloads  240
Abstract
A precondition that uses the special structure of the algebraic system arising from the discretization of a fractional partial differential equation on the red black ordering grid is introduced. Comparison with the numerical solution of the classical Poisson’s equationis considered. A graphical representation for the precondition is illustrated. The performance of our treatment is calculated for different values of the fractional order. The results of the implementation of the SOR and the KSOR with the help of MATLAB are given in compact tables. The value of the relaxation parameter is chosen on the bases of the graphical representation of the behavior of the spectral radius of the iteration matrices. Also, the natural ordering grid is considered.
Keywords
Fractional Boundary Value Problem, SOR, KSOR and Precondition
To cite this article
I. K. Youssef, A. M. Shukur, Precondition for Discretized Fractional Boundary Value Problem, Pure and Applied Mathematics Journal. Vol. 3, No. 1, 2014, pp. 1-6. doi: 10.11648/j.pamj.20140301.11
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