The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation
Applied and Computational Mathematics
Volume 3, Issue 6, December 2014, Pages: 330-336
Received: Nov. 13, 2014;
Accepted: Nov. 27, 2014;
Published: Dec. 31, 2014
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I. K. Youssef, Department of Mathematics, Ain Shams University, Cairo, Egypt
A. M. Shukur, Department of Applied Mathematics, University of Technology, Baghdad, Iraq
The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, the direct way will be used for approximating Time fractional and the expiation of shifted first kind of Chebyshev polynomial will be used to approximate unknown functions, the structure of the systems and the matrices will be fund, the algorithm steps is illustrated, The tables and figures of the results of the implementation by using this method at different values of fractional order will be shown, with the helping of programs of matlab.
I. K. Youssef,
A. M. Shukur,
The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation, Applied and Computational Mathematics.
Vol. 3, No. 6,
2014, pp. 330-336.
G. Caporale, and M. M. Cerrato, Using Chebyshev Polynomials to Approximate Partial Differential Equations, Comput Econ , 2010.
B. Costa, Spectral Methods for Partial Diﬀerential Equations, A Mathem-Journ, Vol. 6, December, 2004.
Z. C. Kuruo˘glu, Weighted-residual methods for the solution of two-particle Lippmann-Schwinger equation without partial-wave decomposition, rXiv, physics.comp-ph, 17 Jul, 2013.
N. Nie, J. Huang, W. Wang, and Y. Tang, Solving spatial-fractional partial differential diffusion equations by spectral method, Journal of Statistical Computation and Simulation, 2013
S. A. Odejide, and Y. A. S. Aregbesola, applications of method of weighted residuals to problems with semi-infinite domain, Rom. Journ. Phys., Vol. 56, Nos. 1-2, P. 14–24, Bucharest, 2009.
R. K. Rektorys, “The method of discretization in time and partial differential equations”, Springer Netherlands, Dec 31, 1982.
Li. Xianjuan, and Xu. Chuanju, A Space-Time Spectral Method for the Time Fractional Diﬀusion Equation, This work supported by National NSF of China , High Performance Scientific-Computation Research Program CB321703, 2005.
J. P. Boyd, Chebyshev and Fourier Spectral Methods, Second Edition, University of Michigan, Ann Arbor, Michigan 48109-2143, 2000.
M. Dalir, and M. Bashour, Applications of Fractional Calculus, App- Math- Scie- Vol. 4, 1021 – 1032 , 2010.