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Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM |
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PP: 2011-2018 |
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Author(s) |
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M. M. Khader,
N. H. Sweilam,
A. M. S. Mahdy,
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Abstract |
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| This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated
by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense.
The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton
iteration method. The method introduces a promising tool for solving many systems of non-linear FDEs. Two numerical examples
are provided to confirm the accuracy and the effectiveness of the proposed methods. Comparisons with the fractional finite difference
method (FDM) and the fourth order Runge-Kutta (RK4) are given. |
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