The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation

I. K. Youssef; A. M. Shukur

doi:doi:10.11648/j.acm.20140306.17

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The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation

I. K. Youssef, A. M. Shukur

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

Received: 13 November 2014 Accepted: 27 November 2014 Published: 31 December 2014

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Abstract

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.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.17
Page(s)	330-336
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Space-Time Fractional Diffusion Equation, Chebyshev-Spectral Method, Finite Difference Method

References

[1]	G. Caporale, and M. M. Cerrato, Using Chebyshev Polynomials to Approximate Partial Differential Equations, Comput Econ , 2010.
[2]	B. Costa, Spectral Methods for Partial Diﬀerential Equations, A Mathem-Journ, Vol. 6, December, 2004.
[3]	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.
[4]	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
[5]	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.
[6]	R. K. Rektorys, “The method of discretization in time and partial differential equations”, Springer Netherlands, Dec 31, 1982.
[7]	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.
[8]	J. P. Boyd, Chebyshev and Fourier Spectral Methods, Second Edition, University of Michigan, Ann Arbor, Michigan 48109-2143, 2000.
[9]	M. Dalir, and M. Bashour, Applications of Fractional Calculus, App- Math- Scie- Vol. 4, 1021 – 1032 , 2010.

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APA Style

I. K. Youssef, A. M. Shukur. (2014). The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Applied and Computational Mathematics, 3(6), 330-336. https://doi.org/10.11648/j.acm.20140306.17

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ACS Style

I. K. Youssef; A. M. Shukur. The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Appl. Comput. Math. 2014, 3(6), 330-336. doi: 10.11648/j.acm.20140306.17

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AMA Style

I. K. Youssef, A. M. Shukur. The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Appl Comput Math. 2014;3(6):330-336. doi: 10.11648/j.acm.20140306.17

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@article{10.11648/j.acm.20140306.17,
  author = {I. K. Youssef and A. M. Shukur},
  title = {The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {330-336},
  doi = {10.11648/j.acm.20140306.17},
  url = {https://doi.org/10.11648/j.acm.20140306.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.17},
  abstract = {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.},
 year = {2014}
}

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TY  - JOUR
T1  - The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation
AU  - I. K. Youssef
AU  - A. M. Shukur
Y1  - 2014/12/31
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AB  - 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.
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Author Information

I. K. Youssef

Department of Mathematics, Ain Shams University, Cairo, Egypt
A. M. Shukur

Department of Applied Mathematics, University of Technology, Baghdad, Iraq

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APA Style

I. K. Youssef, A. M. Shukur. (2014). The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Applied and Computational Mathematics, 3(6), 330-336. https://doi.org/10.11648/j.acm.20140306.17

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ACS Style

I. K. Youssef; A. M. Shukur. The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Appl. Comput. Math. 2014, 3(6), 330-336. doi: 10.11648/j.acm.20140306.17

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AMA Style

I. K. Youssef, A. M. Shukur. The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation. Appl Comput Math. 2014;3(6):330-336. doi: 10.11648/j.acm.20140306.17

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@article{10.11648/j.acm.20140306.17,
  author = {I. K. Youssef and A. M. Shukur},
  title = {The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {330-336},
  doi = {10.11648/j.acm.20140306.17},
  url = {https://doi.org/10.11648/j.acm.20140306.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.17},
  abstract = {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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - The Line Method Combined with Spectral Chebyshev for Space-Time Fractional Diffusion Equation
AU  - I. K. Youssef
AU  - A. M. Shukur
Y1  - 2014/12/31
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140306.17
DO  - 10.11648/j.acm.20140306.17
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 330
EP  - 336
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.17
AB  - 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.
VL  - 3
IS  - 6
ER  -

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